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%I #9 Aug 29 2021 04:32:08
%S 2,16,78,274,814,2058,4752,9930,19574,36186,63924,108078,176672,
%T 279260,429800,645222,947142,1363678,1927532,2681804,3673786,4967774,
%U 6630024,8752102,11422254,14770528,18913112,24022400,30253734,37831400,46953628,57914360,70960394
%N Number of compositions of n with exactly 5 transitions between different parts.
%H Alois P. Heinz, <a href="/A244717/b244717.txt">Table of n, a(n) for n = 9..900</a>
%p b:= proc(n, v) option remember; `if`(n=0, [1, 0$5],
%p add(`if`(v in [0, i], b(n-i, `if`(i<=n-i, i, -1)),
%p [0, b(n-i, `if`(i<=n-i, i, -1))[1..5][]]), i=1..n))
%p end:
%p a:= n-> b(n, 0)[6]:
%p seq(a(n), n=9..60);
%t b[n_, v_] := b[n, v] = If[n == 0, 1, Expand[Sum[b[n - i, i]*
%t If[v == 0 || v == i, 1, x], {i, n}]]];
%t a[n_] := Coefficient[b[n, 0], x, 5];
%t Table[a[n], {n, 9, 60}] (* _Jean-François Alcover_, Aug 29 2021, after A238279 Maple code *)
%Y Column k=5 of A238279.
%K nonn
%O 9,1
%A _Joerg Arndt_ and _Alois P. Heinz_, Jul 04 2014
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