A282566 Number of compositions (ordered partitions) of n into deficient numbers (A005100).

1, 1, 2, 4, 8, 16, 31, 62, 123, 244, 484, 960, 1904, 3777, 7492, 14861, 29478, 58472, 115984, 230064, 456350, 905208, 1795554, 3561628, 7064780, 14013568, 27797058, 55137735, 109370201, 216944729, 430327593, 853589936, 1693165371, 3358531834, 6661922265, 13214467050, 26211974934, 51993593638, 103133540536

Offset: 0

Author

Ilya Gutkovskiy, Feb 18 2017

Keywords

• nonn

Examples

			a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Deficient Number
• Index entries for sequences related to compositions

Crossrefs

Cf. A005100, A097797.

Programs

Mathematica

nmax = 38; CoefficientList[Series[1/(1 - Sum[Boole[DivisorSigma[1, k] < 2 k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

PARI

Vec(1/(1 - sum(k=1, 38, (sigma(k)<2*k)*x^k)) + O(x^39)) \\ Indranil Ghosh, Mar 15 2017

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A005100(k)).