Search: id:A108961
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%I A108961
%S A108961 1,1,2,3,3,5,7,9,12,16,20,26,33,41,51,64,79,97,119,144,175,212,254,305,
%T A108961 365,434,516,612,722,851,1002,1174,1375,1607,1872,2179,2531,2933,3395,
%U A108961 3923,4524,5211,5994,6881,7891,9038,10334,11804,13467,15341,17460,19849
%N A108961 Number of partitions that are "2-close" to being self-conjugate.
%C A108961 Let (a1,a2,a3,...ad:b1,b2,b3,...bd) be the Frobenius symbol for a partition 
               pi of n. Then pi is m-close to being self-conjugate if for all k, 
               |ak-bk| <= m.
%F A108961 Define the Dedekind eta function = q^1/24. Product(1-q^k), k >=1. Then 
               the number of m-close partitions is q^(1/24).(m+2)^2/(1.(2m+4)) (where 
               m denotes eta(q^m)).
%F A108961 Expansion of q^(1/24)*eta(q^4)^2/(eta(q)*eta(q^8)) in powers of q. - 
               Michael Somos Oct 17 2006
%F A108961 Expansion of chi(q^2)*chi(-q) in powers of q where chi() is a Ramanujan 
               theta function. - Michael Somos Oct 17 2006
%F A108961 Euler transform of period 8 sequence [ 1, 1, 1, -1, 1, 1, 1, 0, ...]. 
               - Michael Somos Oct 17 2006
%F A108961 G.f.: Product_{k>0} (1+x^k)*(1+x^(2k))/(1+x^(4k)). - Michael Somos Oct 
               17 2006
%o A108961 (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)^2/ 
               (eta(x+A)*eta(x^8+A)), n))} /* Michael Somos Oct 17 2006 */
%Y A108961 Cf. A000700 for m=0 (self-conjugate), A070047 for m=1, A108962 for m=3.
%Y A108961 Sequence in context: A111865 A042955 A035553 this_sequence A017984 A035066 
               A035068
%Y A108961 Adjacent sequences: A108958 A108959 A108960 this_sequence A108962 A108963 
               A108964
%K A108961 nonn
%O A108961 0,3
%A A108961 John McKay (mckay(AT)cs.concordia.ca), Jul 22 2005

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