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Search: id:A037306
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| A037306 |
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Triangle read by rows: T(n, k) = number of different ways the number n can be expressed as ordered sums of k positive integers, counting only once those ordered sums that can be transformed into each other by a cyclic permutation. |
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1
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| 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 4, 3, 1, 1, 1, 3, 5, 5, 3, 1, 1, 1, 4, 7, 10, 7, 4, 1, 1, 1, 4, 10, 14, 14, 10, 4, 1, 1, 1, 5, 12, 22, 26, 22, 12, 5, 1, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 1, 6, 19, 43, 66, 80, 66, 43, 19, 6, 1, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1
(list; table; graph; listen)
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OFFSET
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1,8
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LINKS
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D. Wasserman, Proof of the symmetry
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EXAMPLE
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T(6,3) = 4, since there are the 4 essentially different ways 1+1+4, 1+2+3, 1+3+2 and 2+2+2 of expressing 6 as a sum of 3 summands (all others can be obtained by cyclically permuting the summands in one of the above sums).
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CROSSREFS
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T(n, 1) + ... + T(n, n) = A008965(n)
Sequence in context: A114087 A008284 A114088 this_sequence A007424 A085424 A088737
Adjacent sequences: A037303 A037304 A037305 this_sequence A037307 A037308 A037309
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KEYWORD
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easy,nonn,tabl,nice
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AUTHOR
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Jens Voss (jens.voss(AT)poet.de), Jun 30 2001
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 11 2002
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