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Search: id:A090723
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| A090723 |
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a(1) = 1; for n > 1, number of partitions of n into distinct odd parts such that the two largest parts differ by 2. |
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+0
2
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| 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 3, 3, 1, 2, 4, 3, 2, 3, 5, 5, 3, 4, 7, 6, 4, 6, 9, 8, 6, 8, 11, 11, 9, 10, 15, 15, 11, 14, 19, 18, 16, 19, 24, 24, 21, 24, 31, 31, 27, 32, 40, 39, 36, 41, 49, 50, 47, 52, 63, 64, 59, 67, 79, 79, 77, 85, 98, 101, 97, 106
(list; graph; listen)
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OFFSET
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1,16
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COMMENT
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Also number of partitions of n such that if k is the largest part, then 1 occurs twice, each of 2,3,...,k-1 occurs a positive even number of times, and k occurs an odd number of times. Example: a(25)=3 because we have [5,4,4,3,3,2,2,1,1], [3,3,3,3,3,2,2,2,2,1,1], and [3,2,2,2,2,2,2,2,2,2,2,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
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FORMULA
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G.f.=x+sum(x^(4k)*product(1+x^(2j-1), j=1..k-1), k=1..infinity). G.f.=sum(x^(k^2)/product(1-x^(2j), j=2..k), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
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EXAMPLE
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a(25)=3 as 25=1+3+5+7+9=5+9+11=1+11+13
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MAPLE
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g:=sum(x^(k^2)/product(1-x^(2*j), j=2..k), k=1..10): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=1..92); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
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PROGRAM
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(PARI) { v=[1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 3, 3, 1, 2, 4, 3, 2]; for (i=2, 30, c=0; forstep (j=i, 1, -2, c+=v[j]); print1(c", ")) }
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CROSSREFS
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a(n) = A000700(n)-A000700(n-2), n>2.
Sequence in context: A094718 A076191 A025861 this_sequence A027357 A078808 A030363
Adjacent sequences: A090720 A090721 A090722 this_sequence A090724 A090725 A090726
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Feb 06 2004
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 10 2004
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