Horizontal shift in tabular environment

Question

My question is the most efficient way to do in tabular environment the last row of the table in the image below. Numbers are shifted horizontally by an half column. thankyou!

Answer 1

Here's a solution that uses the S column type (provided by the siunitx package) to assure that the numeric-data columns are all equally wide. I also suggesting using the \midrule macro (from the booktabs package), instead of \hline, to get well-spaced horizontal rules.

\documentclass{article}
\usepackage{booktabs} % for \midrule macro
\usepackage{siunitx}  % for 'S' column type
\begin{document}

\begin{table}
\centering
\sisetup{table-format=-1.0}
\setlength\arraycolsep{2pt} % default value: 5pt
$\begin{array}{l @{\quad} *{19}{S} }
K & 0 && 1 && 2 && 3 && 4 && 5 && 6 && 7 && 8 && 9\\
\midrule
y_K & 2 && 3 && 5 && 8 && 9 && 9 && 8 && 7 && 7 && 6\\
\midrule
\Delta y_K && 1 && 2 && 3 && 1 && 0 && -1 && -1 && 0 && -1\\
\end{array}$
\end{table}
\end{document}

Answer 2

Here's a (complicated) version that ensures equal width of the columns and computes the differences

\documentclass{article}

\usepackage{xparse,booktabs,array}

\ExplSyntaxOn

\NewDocumentCommand{\difftab}{mmm}
 {% #1=variable name, #2=index name, #3=values
  \christian_diff_tab:nnn { #1 } { #2 } { #3 }
 }

\int_new:N \l_christian_diff_cols_int
\tl_new:N \l_christian_diff_body_tl
\tl_new:N \l__christian_diff_tmp_tl
\seq_new:N \l_christian_diff_data_seq
\seq_new:N \l_christian_diff_diff_seq
\dim_new:N \l__christian_diff_width_dim

\cs_new_protected:Npn \christian_diff_tab:nnn #1 #2 #3
 {
  \dim_zero:N \l__christian_diff_width_dim
  \seq_set_from_clist:Nn \l_christian_diff_data_seq { #3 }
  \seq_map_inline:Nn \l_christian_diff_data_seq
   {
    \tl_set:Nn \l__christian_diff_tmp_tl { ##1 }
    \__christian_diff_measure:
   }
  \seq_clear:N \l_christian_diff_diff_seq
  \int_set:Nn \l_christian_diff_cols_int { \seq_count:N \l_christian_diff_data_seq }
  \tl_clear:N \l_christian_diff_body_tl
  \tl_put_right:Nn \l_christian_diff_body_tl { $#2$ }
  \int_step_inline:nnnn { 1 } { 1 } { \l_christian_diff_cols_int }
   {
    \int_compare:nTF { ##1 > 1 }
     {
      \tl_set:Nx \l__christian_diff_tmp_tl { \int_to_arabic:n { ##1 - 1 } }
      \__christian_diff_measure:
      \tl_put_right:Nx \l_christian_diff_body_tl
       { && \l__christian_diff_tmp_tl }
      %% compute the differences
      \tl_set:Nx \l__christian_diff_tmp_tl
       {
        \int_to_arabic:n 
         {
          \seq_item:Nn \l_christian_diff_data_seq { ##1 }
          -
          \seq_item:Nn \l_christian_diff_data_seq { ##1 - 1 }
         }
       }
      \__christian_diff_measure:
      \seq_put_right:NV \l_christian_diff_diff_seq \l__christian_diff_tmp_tl
     }
     {
      \tl_set:Nx \l__christian_diff_tmp_tl { \int_to_arabic:n { ##1 - 1 } }
      \__christian_diff_measure:
      \tl_put_right:Nx \l_christian_diff_body_tl 
       { & \l__christian_diff_tmp_tl }
     }
   }
  \tl_put_right:Nn \l_christian_diff_body_tl { \tabularnewline\midrule $#1\sb{#2}$ & }
  \tl_put_right:Nx \l_christian_diff_body_tl { \seq_use:Nn \l_christian_diff_data_seq { && } }
  \tl_put_right:Nn \l_christian_diff_body_tl { \tabularnewline\midrule $\Delta #1\sb{#2}$ && }
  \tl_put_right:Nx \l_christian_diff_body_tl { \seq_use:Nn \l_christian_diff_diff_seq { && } }
\tl_show:N \l_christian_diff_body_tl
  %%% make the table
  \use:x
   {
    \exp_not:N \begin {tabular}
     {
      @{}c
      * { \int_to_arabic:n { 1 + 2 * \l_christian_diff_cols_int } }
        { >{\exp_not:N\centering$} p{ \l__christian_diff_width_dim } <{$} @{} }
     }
   }
   \toprule
   \tl_use:N \l_christian_diff_body_tl \tabularnewline
   \bottomrule
  \end{tabular}
 }

\cs_new_protected:Npn \__christian_diff_measure:
 {
  \hbox_set:Nn \l_tmpa_box { $ \l__christian_diff_tmp_tl $ }
  \dim_compare:nT { \box_wd:N \l_tmpa_box > \l__christian_diff_width_dim }
   {
    \dim_set:Nn \l__christian_diff_width_dim { \box_wd:N \l_tmpa_box }
   }
 }
\cs_new_protected:Npn \christian_diff_cell:n #1
 {
  \makebox[\l__christian_diff_width_dim]{ $#1$ }
 }

\ExplSyntaxOff

\begin{document}
\[
\difftab{y}{k}{2, 3, 5, 8, 9, 9, 8, 7, 7, 6}
\]
\[
\difftab{a}{i}{0,1,1,2,3,5,8,13,21}
\]
\end{document}

The main argument is used to compute the differences and also the number of necessary columns. Each item is added to the table, first measuring it so we can pass to tabular the width of the p columns.