I need to shift multiline equations as per attached image

Question

But adding a \hspace doesn't even work and the equations are left justified. Can someone assist me please? Example code is:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{multline}
\begin{split}
[1,2,\ldots,t,\ldots,t+h]\;,\\
[2,\ldots,t+1,\ldots,t+h+1]\;,\\
\vdots\\
[N,\ldots,t+N,\ldots,t+h+N]\;,
\end{split}
 \end{multline}
\end{document}

Answer 1

A simple way to achieve this is to place each line in the second column of an aligned environment, which is itself placed inside an equation environment. Then, the whole structure is centred, with each line beginning at the same point. You can create the necessary indentations using \hspace.

\documentclass{article}
\usepackage{amsmath}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\begin{equation} 
\begin{aligned}
&[1,2,\ldots,t,\ldots,t+h],\\  
&\hspace{50pt}[2,\ldots,t+1,\ldots,t+h+1],\\
&\hspace{130pt}\vdots\\    
&\hspace{100pt}[N,\ldots,t+N,\ldots,t+h+N],   
\end{aligned}    
\end{equation}
\lipsum[2]
\end{document}

Note that it is possible to use \hspace here because the space is not the first item on the line (otherwise you would need \hspace* to prevent the space being discarded). Of course, you will need to adjust the size of the \hspaces manually, so if you need a lot of similar constructions then a more sophisticated approach may be needed.

Incidentally, I don't think you can use split inside a multline (as in your example); if you try you will get the warning

Package amsmath Warning: Cannot use split' here; (amsmath)
trying to recover withaligned' on input line 19.