A027342 Number of partitions of n that do not contain 8 as a part.

1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72, 94, 124, 161, 209, 267, 343, 434, 550, 691, 867, 1079, 1344, 1661, 2051, 2520, 3091, 3773, 4602, 5587, 6774, 8185, 9874, 11873, 14259, 17072, 20411, 24343, 28989, 34440, 40864, 48378, 57198, 67497, 79543

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Column 8 of A175788.

Programs

Mathematica

Table[Count[IntegerPartitions[n],?(FreeQ[#,8]&)],{n,0,50}] (* _Harvey P. Dale, Mar 11 2017 *)

PARI

a(n)=if(n<0,0,polcoeff((1-x^8)/eta(x+x*O(x^n)),n))

Formula

G.f.: (1-x^8) Product_{m>0} 1/(1-x^m).

a(n)=A000041(n)-A000041(n-8).

a(n) ~ 2*Pi * exp(sqrt(2*n/3)*Pi) / (3*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 8*Pi/(2*sqrt(6)))/sqrt(n) + (97/8 + 9/(2*Pi^2) + 12481*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

Extensions

More terms from Benoit Cloitre, Dec 10 2002