A346797 Number of partitions of n into parts congruent to 0, 2 or 5 (mod 7).

1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 3, 4, 3, 7, 4, 9, 6, 10, 11, 11, 17, 13, 22, 19, 25, 29, 28, 42, 34, 53, 46, 61, 67, 69, 92, 83, 115, 109, 133, 149, 152, 198, 182, 243, 233, 282, 309, 324, 398, 385, 485, 483, 563, 621, 648, 784, 768, 944, 947, 1096, 1194, 1262

Offset: 0

Author

Ludovic Schwob, Aug 04 2021

Keywords

• nonn

Examples

			For n=17 the a(17)=6 solutions are 2+2+2+2+2+2+5, 2+2+2+2+2+7, 2+2+2+2+9, 2+5+5+5, 5+5+7 and 5+12.
		

Links

• Ludovic Schwob, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000041, A047386, A274830, A006950, A036820, A036822, A195848, A035363, A195849, A346798.

Programs

Mathematica

CoefficientList[Series[Product[1/((1 - x^(7*k))(1 - x^(7*k-2))(1 - x^(7*k-5))),{k,52}],{x,0,52}],x] (* Stefano Spezia, Aug 04 2021 *)

Formula

G.f.: Product_{k>=1} 1/((1 - x^(7*k))*(1 - x^(7*k-2))*(1 - x^(7*k-5))).

a(n) = a(n-2) + a(n-5) - a(n-11) - a(n-17) + + - - (with a(0)=1 and a(n) = 0 for negative n), where 2, 5, 11, 17, ... is the sequence A274830.

a(n) ~ exp(Pi*sqrt(2*n/7)) / (8*cos(3*Pi/14)*n). - Vaclav Kotesovec, Aug 05 2021