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A171632
Number of compositions of n such that the greatest part is divisible by the number of parts.
3
1, 1, 3, 2, 6, 9, 15, 22, 41, 68, 118, 199, 337, 571, 982, 1677, 2860, 4866, 8284, 14084, 23911, 40544, 68679, 116172, 196249, 331096, 557927, 939008, 1578450, 2650167, 4444505, 7445658, 12460248, 20830822, 34790302, 58049613, 96771364, 161182065
OFFSET
1,3
COMMENTS
G.f.: Sum_{n>=0} Sum_{d|n} ((x^(n+1)-x)^d-(x^n-x)^d)/(x-1)^d.
LINKS
MAPLE
b:= proc(n, t, g) option remember; `if` (n=0, `if` (irem(g, t)=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[g, t] == 0, 1, 0],
Sum[b[n - i, t + 1, Max[i, g]], {i, 1, n}]];
a[n_] := b[n, 0, 0];
Table [a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 11 2021, after Alois P. Heinz *)
CROSSREFS
Cf. A168659.
Sequence in context: A210601 A197493 A300070 * A245609 A365789 A072765
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Dec 13 2009
EXTENSIONS
More terms from Alois P. Heinz, Dec 15 2009
STATUS
approved