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

Author

Vladeta Jovovic, Dec 13 2009

Keywords

• easy
• nonn

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

Crossrefs

Cf. A168659.

Programs

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 *)

Extensions

More terms from Alois P. Heinz, Dec 15 2009