Search: id:A118246
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%I A118246
%S A118246 1,1,2,2,3,4,6,8,10,12,16,20,26,32,40,48,59,72,88,106,128,152,182,216,
%T A118246 258,305,360,422,496,580,680,792,922,1068,1238,1432,1656,1908,2196,2520,
%U A118246 2892,3312,3792,4330,4940,5624,6400,7272,8258,9361,10602,11988,13548
%N A118246 Number of partitions of n such that even parts occur at most once and 
               odd parts occur at most twice.
%C A118246 Also number of partitions of n with no even multiples of 2 and no odd 
               multiples of 3 (i.e. parts equal to 1 or 5 mod 6 and to 2 mod 4). 
               Example: a(7)=8 because we have [7],[6,1],[5,2],[5,1,1],[2,2,2,1],
               [2,2,1,1,1],[2,1,1,1,1,1] and [1,1,1,1,1,1,1].
%H A118246 R. Zumkeller, <a href="b118246.txt">Table of n, a(n) for n = 0..128</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 
               13 2009]
%F A118246 G.f.=product((1+x^(2j-1)+x^(4j-2))(1+x^(2j)), j=1..infinity). G.f.=product([(1-x^(6j-3))(1-x^(4j))]/
               [(1-x^(2j-1))(1-x^(2j))],j=1..infinity). G.f.=1/product((1-x^(1+6j))(1-x^(5+6j))(1-x^(2+4j)), 
               j=0..infinity).
%F A118246 G.f.=product((1+x^j)*(1+x^(2j))/(1+x^(3j)), j=1..infinity). [From Vladeta 
               Jovovic (vladeta(AT)eunet.yu), Jul 24 2009]
%e A118246 a(7)=8 because we have [7],[6,1],[5,2],[5,1,1],[4,3],[4,2,1],[3,3,1] 
               and [3,2,1,1].
%p A118246 g:=product((1+x^(2*j-1)+x^(4*j-2))*(1+x^(2*j)),j=1..50): gser:=series(g,
               x=0,65): seq(coeff(gser,x,n),n=0..60);
%Y A118246 Sequence in context: A005860 A114541 A077114 this_sequence A116902 A066447 
               A035542
%Y A118246 Adjacent sequences: A118243 A118244 A118245 this_sequence A118247 A118248 
               A118249
%K A118246 nonn
%O A118246 0,3
%A A118246 Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2006

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