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Search: id:A114312
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| A114312 |
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Number of partitions of n with at most 3 odd parts. |
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+0
1
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| 1, 2, 3, 4, 6, 8, 12, 14, 22, 24, 38, 39, 63, 62, 102, 95, 159, 144, 244, 212, 366, 309, 540, 442, 784, 626, 1125, 873, 1591, 1209, 2229, 1653, 3089, 2245, 4243, 3019, 5776, 4035, 7806, 5348, 10466, 7051, 13944, 9229, 18454, 12022, 24282, 15565, 31766, 20063
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.=(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)+x^3/(1-x^2)/(1-x^4)/(1-x^6))/Product(1-x^(2*i), i=1..infinity).
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EXAMPLE
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a(6)=8 because we have 6,51,42,411,33,321,222, and 2211 (3111,21111, and 111111 do not qualify).
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MAPLE
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G:=(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)+x^3/(1-x^2)/(1-x^4)/(1-x^6))/Product(1-x^(2*i), i=1..100): Gser:=series(G, x=0, 70): seq(coeff(Gser, x^n), n=1..60);
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CROSSREFS
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Cf. A100824, A100835.
Adjacent sequences: A114309 A114310 A114311 this_sequence A114313 A114314 A114315
Sequence in context: A028815 A014423 A101902 this_sequence A095041 A081029 A034893
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 05 2006
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