A213256 - OEIS

A213256

p(11n+6) where p(k) = number of partitions of k = A000041(k).

%I #22 Nov 08 2023 07:50:19

%S 11,297,3718,31185,204226,1121505,5392783,23338469,92669720,342325709,

%T 1188908248,3913864295,12292341831,37027355200,107438159466,

%U 301384802048,819876908323,2168627105469,5590088317495,14070545699287,34643126322519,83561103925871,197726516681672,459545750448675,1050197489931117

%N p(11n+6) where p(k) = number of partitions of k = A000041(k).

%C It is known that a(n) is divisible by 11 (see A076394).

%H Seiichi Manyama, <a href="/A213256/b213256.txt">Table of n, a(n) for n = 0..1000</a>

%H K. Ono, <a href="https://doi.org/10.1006/jnth.1998.2354">On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function</a>, Journal of Number Theory, Volume 76, Issue 1, May 1999, Pages 62-65.

%H Lasse Winquist, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80105-5">An elementary proof of p(11m+6) == 0 (mod 11)</a>, J. Combinatorial Theory 6 1969 56-59. MR0236136 (38 #4434). - From _N. J. A. Sloane_, Jun 07 2012

%F a(n) = A000041(A017461(n)). - _Omar E. Pol_, Jan 18 2013

%t PartitionsP[11Range[0,30]+6] (* _Paolo Xausa_, Nov 08 2023 *)

%o (PARI) a(n) = numbpart(11*n+6); \\ _Michel Marcus_, Jan 07 2015

%Y Cf. A000041, A076394.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Jun 07 2012