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Search: id:A106351
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| A106351 |
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Triangle read by rows: T(n,k) = number of compositions of n into k parts such that no two adjacent parts are equal. |
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+0
6
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| 1, 1, 0, 1, 2, 0, 1, 2, 1, 0, 1, 4, 2, 0, 0, 1, 4, 7, 2, 0, 0, 1, 6, 9, 6, 1, 0, 0, 1, 6, 15, 14, 3, 0, 0, 0, 1, 8, 21, 24, 15, 2, 0, 0, 0, 1, 8, 28, 46, 30, 10, 1, 0, 0, 0, 1, 10, 35, 66, 68, 30, 4, 0, 0, 0, 0, 1, 10, 46, 100, 119, 76, 24, 2, 0, 0, 0, 0, 1, 12, 54, 138, 204, 168, 69, 14, 1, 0, 0
(list; table; graph; listen)
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OFFSET
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1,5
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LINKS
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A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
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FORMULA
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G.f. 1/(1 - sum(k>0, (-1)^(k+1)*x^k*y^k/(1-x^k)).
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EXAMPLE
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1; 1,0; 1,2,0; 1,2,1,0; 1,4,2,0,0; ...
T(6,3)=7 because the compositions of 6 into 3 parts with no adjacent equal parts are 3+2+1, 3+1+2, 2+3+1, 2+1+3, 1+3+2, 1+2+3, 1+4+1.
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CROSSREFS
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Row sums: A003242. Columns 3-6: A106352-A106355.
Sequence in context: A136266 A054523 A161363 this_sequence A096800 A036586 A092928
Adjacent sequences: A106348 A106349 A106350 this_sequence A106352 A106353 A106354
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Apr 29 2005
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