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A283838
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Irregular triangle read by rows: T(n,k) (n >= 8, 3 <= k <= floor(n/2)-1) = number of binary vectors of length <= n that start with 1^k, 0, end with 1, 0^k, and the factor between 1^k and 0^k does not contain 0^k or 1^k.
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3
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1, 3, 5, 1, 9, 3, 16, 7, 1, 26, 13, 3, 43, 25, 7, 1, 71, 47, 15, 3, 115, 88, 29, 7, 1, 187, 162, 57, 15, 3, 304, 299, 111, 31, 7, 1, 492, 551, 215, 61, 15, 3, 797, 1015, 416, 121, 31, 7, 1, 1291, 1867, 802, 239, 63, 15, 3, 2089, 3435, 1547, 471, 125, 31, 7, 1, 3381, 6319, 2983, 927, 249, 63, 15, 3
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OFFSET
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8,2
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LINKS
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EXAMPLE
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Triangle begins:
1,
3,
5, 1,
9, 3,
16, 7, 1,
26, 13, 3,
43, 25, 7, 1,
71, 47, 15, 3,
115, 88, 29, 7, 1,
187, 162, 57, 15, 3,
304, 299, 111, 31, 7, 1,
492, 551, 215, 61, 15, 3,
797, 1015, 416, 121, 31, 7, 1,
1291, 1867, 802, 239, 63, 15, 3,
2089, 3435, 1547, 471, 125, 31, 7, 1,
3381, 6319, 2983, 927, 249, 63, 15, 3,
5472, 11624, 5751, 1824, 495, 127, 31, 7, 1,
...
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MATHEMATICA
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gf[k_] := x^(2k)(x-x^k)^2 / ((1-x)(1-x^k)(1-2x+x^k));
T[n_, k_] := SeriesCoefficient[gf[k], {x, 0, n}];
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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