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a(n) = p(11n+6)/11 where p(n) = number of partitions of n (A000041).
10

%I #33 Oct 17 2016 09:35:51

%S 1,27,338,2835,18566,101955,490253,2121679,8424520,31120519,108082568,

%T 355805845,1117485621,3366123200,9767105406,27398618368,74534264393,

%U 197147918679,508189847045,1279140518117,3149375120229,7596463993261

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

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

%H Seiichi Manyama, <a href="/A076394/b076394.txt">Table of n, a(n) for n = 0..1000</a>

%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))/11 = A213256(n)/11. - _Omar E. Pol_, Jan 18 2013

%p seq(combinat:-numbpart(11*n+6)/11, n=0..30); # _Robert Israel_, Jan 07 2015

%t PartitionsP[(11*Range[0,30]+6)]/11 (* _Harvey P. Dale_, May 28 2015 *)

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

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

%K nonn

%O 0,2

%A _Jeff Burch_, Nov 07 2002