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A244716 Number of compositions of n with exactly 4 transitions between different parts.

%I A244716 #9 Aug 29 2021 04:32:46
%S A244716 1,6,31,99,278,654,1390,2714,4927,8531,13963,22134,33767,50283,72470,
%T A244716 102891,142375,194202,260093,343973,447906,577636,735540,928009,
%U A244716 1159312,1436145,1765079,2152787,2608321,3137866,3755214,4464420,5284570,6216275,7287298,8494233
%N A244716 Number of compositions of n with exactly 4 transitions between different parts.
%H A244716 Alois P. Heinz, <a href="/A244716/b244716.txt">Table of n, a(n) for n = 7..900</a>
%p A244716 b:= proc(n, v) option remember; `if`(n=0, [1, 0$4],
%p A244716       add(`if`(v in [0, i], b(n-i, `if`(i<=n-i, i, -1)),
%p A244716       [0, b(n-i, `if`(i<=n-i, i, -1))[1..4][]]), i=1..n))
%p A244716     end:
%p A244716 a:= n-> b(n, 0)[5]:
%p A244716 seq(a(n), n=7..60);
%t A244716 b[n_, v_] := b[n, v] = If[n == 0, 1, Expand[Sum[b[n - i, i]*
%t A244716      If[v == 0 || v == i, 1, x], {i, n}]]];
%t A244716 a[n_] := Coefficient[b[n, 0], x, 4];
%t A244716 Table[a[n], {n, 7, 60}] (* _Jean-François Alcover_, Aug 29 2021, after A238279 Maple code *)
%Y A244716 Column k=4 of A238279.
%K A244716 nonn
%O A244716 7,2
%A A244716 _Joerg Arndt_ and _Alois P. Heinz_, Jul 04 2014