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Search: id:A126683
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| A126683 |
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a(n) is the number of partitions of the n-th triangular number n(n+1)/2 into distinct odd parts. |
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1
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| 1, 1, 1, 2, 4, 8, 16, 33, 68, 144, 312, 686, 1523, 3405, 7652, 17284, 39246, 89552, 205253, 472297, 1090544, 2525904, 5867037, 13663248, 31896309, 74628130, 174972341, 411032475, 967307190, 2280248312, 5383723722, 12729879673
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OFFSET
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1,4
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COMMENT
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Also the number of self-conjugate partitions of the n-th triangular number.
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EXAMPLE
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The 5th triangular number is 15. Writing this as a sum of distinct odd numbers: 15 = 11 + 3 + 1 = 9 + 5 + 1 = 7 + 5 + 3 are all the possibilities. So a(5) = 4.
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MAPLE
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g:=product(1+x^(2*j+1), j=0..900): seq(coeff(g, x, n*(n+1)/2), n=1..40); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
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CROSSREFS
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Sequences A066655 and A104383 do the same thing for triangular numbers, with partitions or distinct partitions. Sequences A072213 and A072243 are analogues for squares rather than triangular numbers.
Sequence in context: A119610 A121485 A098588 this_sequence A005821 A004149 A129986
Adjacent sequences: A126680 A126681 A126682 this_sequence A126684 A126685 A126686
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KEYWORD
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nonn
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AUTHOR
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Moshe Newman (mshnoiman(AT)hotmail.com), Feb 15 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
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