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Search: id:A125101
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| A125101 |
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T(n,k)=k*binomial(n-1,k-1) + fibonacci(k)*binomial(n-1,k) (1<=k<=n). |
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1
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| 1, 2, 2, 3, 5, 3, 4, 9, 11, 4, 5, 14, 26, 19, 5, 6, 20, 50, 55, 30, 6, 7, 27, 85, 125, 105, 44, 7, 8, 35, 133, 245, 280, 182, 62, 8, 9, 44, 196, 434, 630, 560, 300, 85, 9, 10, 54, 276, 714, 1260, 1428, 1056, 477, 115, 10, 11, 65, 375, 1110, 2310, 3192, 3030, 1905, 745, 155
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next to left column = A000096 starting (2, 5, 9, 14...). Next column going to the right = A051925 starting (3, 11, 26, 50,...). Row sums are 1, 4, 11, 28, 69, 167, 400,...
Binomial transform of the bidiagonal matrix with (1,2,3...) in the main diagonal and the Fibonacci numbers (1,1,2,3,5,8,...) in the subdiagonal.
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EXAMPLE
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First few rows of the triangle are:
1;
2, 2;
3, 5, 3;
4, 9, 11, 4;
5, 14, 26, 19, 5;
6, 20, 50, 55, 30, 6;
7, 27, 85, 125, 105, 44, 7;
8, 35, 133, 245, 280, 182, 62, 8;
...
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MAPLE
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with(combinat): T:=(n, k)->k*binomial(n-1, k-1)+fibonacci(k)*binomial(n-1, k): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000096, A051925.
Sequence in context: A128141 A014430 A124727 this_sequence A047666 A067330 A132403
Adjacent sequences: A125098 A125099 A125100 this_sequence A125102 A125103 A125104
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 20 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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