A346797 - OEIS

%I #21 Aug 05 2021 16:25:00

%S 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,

%T 34,53,46,61,67,69,92,83,115,109,133,149,152,198,182,243,233,282,309,

%U 324,398,385,485,483,563,621,648,784,768,944,947,1096,1194,1262

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

%H Ludovic Schwob, <a href="/A346797/b346797.txt">Table of n, a(n) for n = 0..10000</a>

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

%F 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.

%F a(n) ~ exp(Pi*sqrt(2*n/7)) / (8*cos(3*Pi/14)*n). - _Vaclav Kotesovec_, Aug 05 2021

%e 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.

%t 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 *)

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

%K nonn

%O 0,8

%A _Ludovic Schwob_, Aug 04 2021