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Search: id:A100835
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| A100835 |
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Number of partitions of n with at most 2 odd parts. |
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+0
2
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| 1, 2, 2, 4, 4, 8, 7, 14, 12, 24, 19, 39, 30, 62, 45, 95, 67, 144, 97, 212, 139, 309, 195, 442, 272, 626, 373, 873, 508, 1209, 684, 1653, 915, 2245, 1212, 3019, 1597, 4035, 2087, 5348, 2714, 7051, 3506, 9229, 4508, 12022, 5763, 15565, 7338, 20063, 9296, 25722
(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))/Product(1-x^(2*i), i=1..infinity). More generally, g.f. for number of partitions of n with at most k odd parts is (1+Sum(x^i/Product(1-x^(2*j), j=1..i), i=1..k))/Product(1-x^(2*i), i=1..infinity).
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EXAMPLE
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a(5)=4 because we have 5,41,32 and 221 (311,2111 and 11111 do not qualify).
a(5)=4 because we have [5], [4,1], [3,2] and [2,2,1] (the partitions [3,1,1], [2,1,1,1] and [1,1,1,1,1] 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))/Product(1-x^(2*i), i=1..100): Gser:=series(G, x=0, 70): seq(coeff(Gser, x^n), n=1..60); (Deutsch)
g:=(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4))/product(1-x^(2*i), i=1..40): gser:=series(g, x=0, 60): seq(coeff(gser, x^n), n=1..55); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006
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CROSSREFS
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Cf. A000070, A008951, A000097, A000098, A000710.
Sequence in context: A139210 A008330 A138219 this_sequence A120541 A059867 A046971
Adjacent sequences: A100832 A100833 A100834 this_sequence A100836 A100837 A100838
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 13 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 05 2006
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006
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