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Search: id:A102426
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| A102426 |
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Triangle read by rows giving coefficients of polynomials defined by F(0)=0, F(1)=1, F(n+1) = F(n) + x*F(n-1). |
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+0
5
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| 0, 1, 1, 1, 1, 2, 1, 1, 3, 1, 3, 4, 1, 1, 6, 5, 1, 4, 10, 6, 1, 1, 10, 15, 7, 1, 5, 20, 21, 8, 1, 1, 15, 35, 28, 9, 1
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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F(n) + 2x * F(n-1) gives Lucas polynomials (cf. A034807). - Maxim Krikun (krikun(AT)iecn.u-nancy.fr), Jun 24 2007
Essentially the same as A098925. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 30 2008]
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FORMULA
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Alternatively, as n is even or odd: T(n-2, k) + T(n-1, k-1) = T(n, k) T(n-2, k) + T(n-1, k) = T(n, k)
T(n, k)=binomial(floor(n/2)+k, floor((n-1)/2-k) - Paul Barry (pbarry(AT)wit.ie), Jun 22 2005
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EXAMPLE
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The first few polynomials are:
0
1
1
x + 1
2x + 1
x^2 + 3x + 1
3x^2 + 4x + 1
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CROSSREFS
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Upward diagonals sums are A062200. Downward rows are A102427. Row sums are A000045. Row terms reversed = A011973. Also A102427, A102428, A102429.
Sequence in context: A121560 A136405 A035667 this_sequence A092865 A098925 A052920
Adjacent sequences: A102423 A102424 A102425 this_sequence A102427 A102428 A102429
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Russell Walsmith (russw(AT)lycos.com), Jan 08 2005
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