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A080850
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Number triangle related to a problem of Knuth.
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0
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1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 5, 5, 6, 4, 1, 11, 10, 11, 10, 5, 1, 22, 21, 21, 21, 15, 6, 1, 43, 43, 42, 42, 36, 21, 7, 1, 85, 86, 85, 84, 78, 57, 28, 8, 1, 170, 171, 171, 169, 162, 135, 85, 36, 9, 1, 341, 341, 342, 340, 331, 297, 220, 121, 45, 10, 1, 683, 682, 683, 671, 628, 517
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OFFSET
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1,5
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COMMENTS
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In lower-triangular form, the columns are the binomial transforms of the sequences with g.f. x^(k-1)/(1-x^3). The first three columns are A024493, A024494, A024495.
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LINKS
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FORMULA
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T(n, 1) = A024493(n). T(n, k)=0, k>n, T(n, n)=1. T(n, k) = T(n-1, k-1)+T(n-1, k).
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EXAMPLE
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Rows are {1}, {1,1}, {1,2,1}, {2,3,3,1}, {5,5,6,4,1}, {11,10,11,10,5,1}...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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