A171628 Number of compositions of n such that the smallest part is divisible by the number of parts.

1, 1, 1, 2, 3, 3, 3, 4, 6, 8, 11, 15, 19, 22, 25, 30, 37, 47, 62, 83, 108, 136, 168, 205, 247, 295, 354, 429, 524, 642, 789, 972, 1196, 1466, 1789, 2173, 2625, 3155, 3778, 4515, 5391, 6437, 7692, 9201, 11014, 13186, 15780, 18865, 22516, 26818, 31871, 37791

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..900

Formula

G.f.: Sum_{n>=0} [Sum_{d|n} x^(n*d)*(1-x^d)/(1-x)^d].

Maple

b:= proc(n, t, g) option remember; `if` (n=0, `if` (irem(g, t)=0, 1, 0), add (b(n-i, t+1, min(i, g)), i=1..n)) end: a:= n-> b(n, 0, infinity): seq (a(n), n=1..60); # Alois P. Heinz, Dec 15 2009
A171628 := proc(n) local g, k; g := 0 ; for k from 0 to n do g := g+add (x^(k*d)*(1-x^d)/(1-x)^d, d=numtheory[divisors](k)) ; g := expand(g) ; end do ; coeftayl(g, x=0, n) ; end proc: seq(A171628(n), n=1..60) ; # R. J. Mathar, Dec 14 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, Min[i, g]], {i, n}]];
a[n_] := b[n, 0, Infinity];
Array[a, 60] (* Jean-François Alcover, May 23 2020, after Alois P. Heinz *)

Crossrefs

Cf. A168656, A171625.

Sequence in context: A327720 A327718 A035581 * A205566 A064338 A197592

Adjacent sequences: A171625 A171626 A171627 * A171629 A171630 A171631

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 13 2009

Extensions

More terms from R. J. Mathar and Alois P. Heinz, Dec 14 2009

Status

approved