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A109223
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Number triangle related to the Fibonacci polynomials.
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3
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1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 6, 5, 7, 1, 1, 1, 6, 15, 7, 9, 1, 1, 1, 10, 15, 28, 9, 11, 1, 1, 1, 10, 35, 28, 45, 11, 13, 1, 1, 1, 15, 35, 84, 45, 66, 13, 15, 1, 1, 1, 15, 70, 84, 165, 66, 91, 15, 17, 1, 1, 1, 21, 70, 210, 165, 286, 91, 120, 17, 19, 1, 1, 1, 21, 126, 210
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Riordan array (1/(1-x),x/(1-x^2)^2). Row-reversal of number triangle A109221. Diagonals form a repeated version of A054142. Row sums are A109222. Diagonal sums are A094967.
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FORMULA
| T(n,k) = binomial(floor((n+k)/2)+k, 2*k)
T(n,k) = A065941(n+k,n-k) [Johannes W. Meijer, Aug 14 2011]
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EXAMPLE
| Rows begin
1;
1,1;
1,1,1;
1,3,1,1;
1,3,5,1,1;
1,6,5,7,1,1;
1,6,15,7,9,1,1;
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MAPLE
| A109223 := proc(n, k): binomial(floor((n+k)/2)+k, 2*k) end: seq(seq(A109223(n, k), k=0..n), n=0..11); # [Johannes W. Meijer, Aug 14 2011]
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CROSSREFS
| Sequence in context: A016733 A060234 A131270 * A176246 A016466 A055210
Adjacent sequences: A109220 A109221 A109222 * A109224 A109225 A109226
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 22 2005
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