A076394 a(n) = p(11n+6)/11 where p(n) = number of partitions of n (A000041).

1, 27, 338, 2835, 18566, 101955, 490253, 2121679, 8424520, 31120519, 108082568, 355805845, 1117485621, 3366123200, 9767105406, 27398618368, 74534264393, 197147918679, 508189847045, 1279140518117, 3149375120229, 7596463993261

Offset: 0

Author

Jeff Burch, Nov 07 2002

Keywords

• nonn

Comments

That p(11n+6) == 0 (mod 11) is one of the congruences stated by Ramanujan. - Omar E. Pol, Jan 18 2013

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Lasse Winquist, An elementary proof of p(11m+6) == 0 (mod 11), J. Combinatorial Theory 6 1969 56--59. MR0236136 (38 #4434). - From _N. J. A. Sloane_, Jun 07 2012

Crossrefs

Cf. A000041, A071734, A071746, A213256, A182668.

Programs

Maple

seq(combinat:-numbpart(11*n+6)/11, n=0..30); # Robert Israel, Jan 07 2015

Mathematica

PartitionsP[(11*Range[0,30]+6)]/11 (* Harvey P. Dale, May 28 2015 *)

PARI

a(n) = numbpart(11*n+6)/11; \\ Michel Marcus, Jan 07 2015

Formula

a(n) = A000041(A017461(n))/11 = A213256(n)/11. - Omar E. Pol, Jan 18 2013