Consider an array of numbers
$ \color{#C00000}{1}\ \hphantom{7\ 6\ 5\ 4\ 7\ 3\ 5\ 7\ 2\ 7\ 5\ 3\ 7\ 4\ 5\ 6\ 7\ }\color{#C00000}{1}\\ 1\ \hphantom{7\ 6\ 5\ 4\ 7\ 3\ 5\ 7\ }\color{#C00000}{2}\ \hphantom{7\ 5\ 3\ 7\ 4\ 5\ 6\ 7\ }1\\ 1\ \hphantom{7\ 6\ 5\ 4\ 7\ }\color{#C00000}{3}\ \hphantom{5\ 7\ }2\ \hphantom{7\ 5\ }\color{#C00000}{3}\ \hphantom{7\ 4\ 5\ 6\ 7\ }1\\ 1\ \hphantom{7\ 6\ 5\ }\color{#C00000}{4}\ \hphantom{7\ }3\ \hphantom{5\ 7\ }2\ \hphantom{7\ 5\ }3\ \hphantom{7\ }\color{#C00000}{4}\ \hphantom{5\ 6\ 7\ }1\\ 1\ \hphantom{7\ 6\ }\color{#C00000}{5}\ 4\ \hphantom{7\ }3\ \color{#C00000}{5}\ \hphantom{7\ }2\ \hphantom{7\ }\color{#C00000}{5}\ 3\ \hphantom{7\ }4\ \color{#C00000}{5}\ \hphantom{6\ 7\ }1\\ 1\ \hphantom{7\ }\color{#C00000}{6}\ 5\ 4\ \hphantom{7\ }3\ 5\ \hphantom{7\ }2\ \hphantom{7\ }5\ 3\ \hphantom{7\ }4\ 5\ \color{#C00000}{6}\ \hphantom{7\ }1\\ 1\ \color{#C00000}{7}\ 6\ 5\ 4\ \color{#C00000}{7}\ 3\ 5\ \color{#C00000}{7}\ 2\ \color{#C00000}{7}\ 5\ 3\ \color{#C00000}{7}\ 4\ 5\ 6\ \color{#C00000}{7}\ 1\\ $ The pattern: starting from 1 1, every consecutive natural number n will be inserted between two numbers beside each other whose sum equals n (2 between 1 1, 3 between 1 2, 4 between 1 3, etc )
You can see this pattern displayed above.
My question is: what is a(n) - the number of times we will have to write n in the nth row ?
My attempt: trying to find recursive formula between a(n) and a(n+1), but this seems hard.