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A171634
Number of compositions of n such that the number of parts is divisible by the greatest part.
2
1, 1, 3, 2, 8, 13, 21, 38, 89, 173, 302, 545, 1109, 2309, 4564, 8601, 16188, 31365, 62518, 125813, 251119, 493123, 956437, 1854281, 3633938, 7218166, 14444539, 28868203, 57300450, 112921744, 221760513, 436117749, 861764899, 1711773936
OFFSET
1,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..715 (terms 1..250 from Alois P. Heinz)
FORMULA
G.f.: Sum_{n>=0} Sum_{d|n} ((x^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n.
MAPLE
b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(t, g)=0, 1, 0), add(b(n-i, t+1, max(i, g)), i=1..n)) end: a:= n-> b(n, 0, 0): seq(a(n), n=1..40); # Alois P. Heinz, Dec 15 2009
MATHEMATICA
b[n_, t_, g_] := b[n, t, g] = If[n == 0, If [Mod[t, g] == 0, 1, 0], Sum[b[n - i, t + 1, Max[i, g]], {i, 1, n}]];
a[n_] := b[n, 0, 0];
Array[a, 40] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A373288 A301903 A165660 * A107300 A285787 A047946
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Dec 13 2009
EXTENSIONS
More terms from Alois P. Heinz, Dec 15 2009
STATUS
approved