A171632 Number of compositions of n such that the greatest part is divisible by the number of parts.

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

Alois P. Heinz, Table of n, a(n) for n = 1..250

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

Adjacent sequences: A171629 A171630 A171631 * A171633 A171634 A171635

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 13 2009

Extensions

More terms from Alois P. Heinz, Dec 15 2009

Status

approved