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A161294 Number of partitions of n into numbers not divisible by 4 where every part appears at least 3 times. 1

%I

%S 0,0,1,1,1,2,1,2,3,3,3,6,5,6,10,8,9,15,13,16,22,20,24,33,32,36,47,48,

%T 53,71,68,77,100,99,112,140,138,158,194,199,219,268,275,305,369,377,

%U 416,501,514,572,671,693,768,898,935,1028,1189,1245,1364,1576,1642,1798,2063

%N Number of partitions of n into numbers not divisible by 4 where every part appears at least 3 times.

%H R. H. Hardin, <a href="/A161294/b161294.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: -1 + (Product_{j>=1} (1 + x^(3j)/(1-x^j))/Product_{j>=1} (1 + x^(12j)/(1-x^(4j))). - _Emeric Deutsch_, Jun 21 2009

%e a(13)=5 because we have (3^3)(1^4), (2^5)(1^3), (2^4)(1^5), (2^3)(1^7), and 1^(13). - _Emeric Deutsch_, Jun 21 2009

%p g := -1+(product(1+x^(3*j)/(1-x^j), j = 1 .. 40))/(product(1+x^(12*j)/(1-x^(4*j)), j = 1 .. 40)): gser := series(g, x = 0, 70): seq(coeff(gser, x, n), n = 2 .. 68); # _Emeric Deutsch_, Jun 21 2009

%K nonn

%O 1,6

%A _R. H. Hardin_, Jun 06 2009

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Last modified January 18 19:44 EST 2022. Contains 350455 sequences. (Running on oeis4.)