A199885 Number of compositions of n such that the greatest part is not divisible by the number of parts.

0, 1, 1, 6, 10, 23, 49, 106, 215, 444, 906, 1849, 3759, 7621, 15402, 31091, 62676, 126206, 253860, 510204, 1024665, 2056608, 4125625, 8272436, 16580967, 33223336, 66550937, 133278720, 266857006, 534220745, 1069297319, 2140037990, 4282507048, 8569103770

Offset

1,4

Links

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

Formula

G.f.: Sum_{n>0} (2^(n-1)*x^n-Sum_{d|n} ((x^(n+1)-x)^d-(x^n-x)^d)/(x-1)^d).

a(n) = A000079(n-1) - A171632(n).

Example

a(4) = 6: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1].

Maple

b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(g, t)=0, 0, 1), 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);

Mathematica

b[n_, t_, g_] := b[n, t, g] = If[n == 0, If[Mod[g, t] == 0, 0, 1], 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, Nov 05 2014, after Alois P. Heinz *)

Crossrefs

Cf. A000079, A171632, A200727.

Sequence in context: A079426 A212161 A132994 * A024499 A143236 A107306

Adjacent sequences: A199882 A199883 A199884 * A199886 A199887 A199888

Keyword

nonn

Author

Alois P. Heinz, Nov 11 2011

Status

approved