A199884 Number of compositions of n such that the number of parts is not divisible by the greatest part.

0, 1, 1, 6, 8, 19, 43, 90, 167, 339, 722, 1503, 2987, 5883, 11820, 24167, 49348, 99707, 199626, 398475, 797457, 1604029, 3237867, 6534327, 13143278, 26336266, 52664325, 105349525, 211135006, 423949168, 851981311, 1711365899, 3433202397, 6878160656, 13768314357

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^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n).

a(n) = A000079(n-1) - A171634(n).

Example

a(5) = 8: [1,2,2], [1,4], [2,1,2], [2,2,1], [2,3], [3,2], [4,1], [5].

Maple

b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(t, g)=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[t, g] == 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, A171634, A200727.

Sequence in context: A173975 A349770 A349225 * A028331 A279729 A357946

Adjacent sequences: A199881 A199882 A199883 * A199885 A199886 A199887

Keyword

nonn

Author

Alois P. Heinz, Nov 11 2011

Status

approved