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A244715 Number of compositions of n with exactly 3 transitions between different parts.

%I A244715 #9 Aug 29 2021 04:32:54
%S A244715 2,10,36,86,200,374,680,1122,1796,2694,3954,5600,7752,10448,13798,
%T A244715 18072,23032,29218,36390,45044,54870,66852,79790,95550,112662,132938,
%U A244715 154752,180614,207764,239784,273898,312922,354240,401826,451598,508134,567756,634634,705506
%N A244715 Number of compositions of n with exactly 3 transitions between different parts.
%H A244715 Alois P. Heinz, <a href="/A244715/b244715.txt">Table of n, a(n) for n = 6..900</a>
%p A244715 b:= proc(n, v) option remember; `if`(n=0, [1, 0$3],
%p A244715       add(`if`(v in [0, i], b(n-i, `if`(i<=n-i, i, -1)),
%p A244715       [0, b(n-i, `if`(i<=n-i, i, -1))[1..3][]]), i=1..n))
%p A244715     end:
%p A244715 a:= n-> b(n, 0)[4]:
%p A244715 seq(a(n), n=6..60);
%t A244715 b[n_, v_] := b[n, v] = If[n == 0, 1, Expand[Sum[b[n - i, i]*
%t A244715      If[v == 0 || v == i, 1, x], {i, n}]]];
%t A244715 a[n_] := Coefficient[b[n, 0], x, 3];
%t A244715 Table[a[n], {n, 6, 60}] (* _Jean-François Alcover_, Aug 29 2021, after A238279 Maple code *)
%Y A244715 Column k=3 of A238279.
%K A244715 nonn
%O A244715 6,1
%A A244715 _Joerg Arndt_ and _Alois P. Heinz_, Jul 04 2014