A027338 Number of partitions of n that do not contain 4 as a part.

1, 1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 196, 250, 314, 396, 495, 617, 765, 948, 1166, 1434, 1755, 2143, 2607, 3168, 3832, 4631, 5578, 6706, 8041, 9628, 11494, 13705, 16302, 19361, 22946, 27159, 32076, 37837, 44551, 52384, 61493

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Column 4 of A175788.

Programs

PARI

a(n)=if(n<0,0,polcoeff((1-x^4)/eta(x+x*O(x^n)),n))

Formula

G.f.: (1-x^4) Product_{m>0} 1/(1-x^m).

a(n) = A000041(n)-A000041(n-4).

a(n) ~ Pi * exp(sqrt(2*n/3)*Pi) / (3*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 4*Pi/(2*sqrt(6)))/sqrt(n) + (49/8 + 9/(2*Pi^2) + 3169*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

Extensions

More terms from Benoit Cloitre, Dec 10 2002