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Search: id:A069713
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| A069713 |
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As a square array T(n,k) by antidiagonals, number of ways of partitioning k into up to n parts each no more than 5, or into up to 5 parts each no more than n; as a triangle t(n,k), number of ways of partitioning n into exactly k parts each no more than 6 (i.e. of arranging k indistinguishable standard dice to produce a total of n). |
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| 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 3, 3, 2, 1, 1, 0, 0, 3, 4, 3, 2, 1, 1, 0, 0, 3, 5, 5, 3, 2, 1, 1, 0, 0, 2, 6, 6, 5, 3, 2, 1, 1, 0, 0, 2, 6, 8, 7, 5, 3, 2, 1, 1, 0, 0, 1, 6, 9, 9, 7, 5, 3, 2, 1, 1, 0, 0, 1, 6, 11, 11, 10, 7, 5, 3, 2, 1, 1, 0, 0, 0, 5, 11, 14, 12, 10, 7, 5
(list; table; graph; listen)
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OFFSET
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0,13
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FORMULA
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If k<6 T(n, k)=A068914(n, k). T(n, k)=T(n, 5n-k); t(n, k)=t(7n-k, k). T([5n/2], n)=t(n, [7n/2])=A001975(n).
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EXAMPLE
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As square array, rows start: 1,0,0,0,0,0,...; 1,1,1,1,1,1,...; 1,1,2,2,3,3,...; 1,1,2,3,4,5,...; 1,1,2,3,5,6,...; 1,1,2,3,5,7,...; etc. As triangle, rows start: 1; 0,1; 0,1,1; 0,1,1,1; 0,1,2,1,1; 0,1,2,2,1,1; 0,1,3,3,2,1,1; etc. T(3,7)=6 since 7 can be written as 5+2, 5+1+1, 4+3, 4+2+1, 3+3+1, 3+2+2; or alternatively as 2+2+1+1+1, 3+1+1+1, 2+2+2+1, 3+2+1+1, 3+2+2, 3+3+1. t(10,3)=6 since 10 can be written as 6+3+1, 6+2+2, 5+4+1, 5+3+2, 4+4+2, 4+3+3.
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CROSSREFS
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Cf. A061676 for a similar triangle, though with distinguishable dice (and a different offset). Anti-diagonal sums of T(n, k), i.e. row sums (over k) of t(n, k), are A001402. First 22 terms are same as A068914 (see formula).
Sequence in context: A116375 A054078 A029400 this_sequence A072233 A116598 A068914
Adjacent sequences: A069710 A069711 A069712 this_sequence A069714 A069715 A069716
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 01 2002
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