A290137 Number of compositions (ordered partitions) of n into nonprime squarefree parts (A000469).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 30, 41, 55, 73, 96, 128, 173, 235, 317, 426, 570, 763, 1023, 1375, 1848, 2484, 3337, 4482, 6017, 8077, 10843, 14562, 19560, 26276, 35292, 47392, 63632, 85443, 114741, 154098, 206957, 277941, 373254, 501244, 673121, 903945, 1213935, 1630246, 2189330

Offset: 0

Author

Ilya Gutkovskiy, Jul 20 2017

Keywords

• nonn

Examples

			a(8) = 4 because we have [6, 1, 1], [1, 6, 1], [1, 1, 6] and [1, 1, 1, 1, 1, 1, 1, 1].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A000469, A239508, A239509, A280194.

Programs

Mathematica

nmax = 53; CoefficientList[Series[1/(1 - Sum[Boole[SquareFreeQ[k] && PrimeNu[k] != 1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A000469(k)).