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Search: id:A066633
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| A066633 |
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Triangle T(n,k), n>=1, 1<=k<=n, giving number of k's in all partitions of n. |
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16
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| 1, 2, 1, 4, 1, 1, 7, 3, 1, 1, 12, 4, 2, 1, 1, 19, 8, 4, 2, 1, 1, 30, 11, 6, 3, 2, 1, 1, 45, 19, 9, 6, 3, 2, 1, 1, 67, 26, 15, 8, 5, 3, 2, 1, 1, 97, 41, 21, 13, 8, 5, 3, 2, 1, 1, 139, 56, 31, 18, 12, 7, 5, 3, 2, 1, 1, 195, 83, 45, 28, 17, 12, 7, 5, 3, 2, 1, 1, 272, 112, 63, 38, 25, 16, 11, 7, 5
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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1; 2,1; 4,1,1; 7,3,1,1; 12,4,2,1,1;....
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LINKS
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Eric Weisstein's World of Mathematics, Elder's Theorem
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FORMULA
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T(n, 1) + ... + T(n, n) = A006128(n).
G.f. for the number of k's in all partitions of n is x^k/(1-x^k)*Product_{m>=1} 1/(1-x^m). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 15 2002
T(n, k) = Sum_{j<n, j=n (mod k)} P(j), P(j) = number of partitions of j, P(0) = 1 - Jose Luis Arregui (arregui(AT)posta.unizar.es), Apr 05 2002
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EXAMPLE
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For n = 3, k = 1; 3 = 2+1 = 1+1+1. T(3,1) = (zero 1's) + (one 1's) + (three 1's), so T(3,1) = 4.
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CROSSREFS
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Diagonals: A000070, A024786-A024794.
Sequence in context: A105260 A099510 A137633 this_sequence A088443 A117352 A137710
Adjacent sequences: A066630 A066631 A066632 this_sequence A066634 A066635 A066636
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 09 2002
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 11 2002
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