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A081576
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Square array of binomial transforms of Fibonacci numbers, read by antidiagonals.
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0
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0, 0, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 5, 8, 3, 0, 1, 7, 20, 21, 5, 0, 1, 9, 38, 75, 55, 8, 0, 1, 11, 62, 189, 275, 144, 13, 0, 1, 13, 92, 387, 905, 1000, 377, 21, 0, 1, 15, 128, 693, 2305, 4256, 3625, 987, 34, 0, 1, 17, 170, 1131, 4955, 13392, 19837, 13125, 2584, 55
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Rows include A000045, A001906, A030191, A081573, A081574, A081575. Row are solutions of the recurrence a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2),a(0)=0,a(1)=1.
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FORMULA
| Rows are successive binomial transforms of F(n). T(n, k)=((sqrt(5)/2 + (2*k + 1)/2)^n - ((2*k + 1)/2 - sqrt(5)/2)^n)/sqrt(5)
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EXAMPLE
| Rows start
0 1 1 2 3 5 ...
0 1 3 8 21 55 ...
0 1 5 20 75 275 ...
0 1 7 38 189 905 ...
0 1 9 62 387 2305 ...
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CROSSREFS
| Sequence in context: A151844 A008783 A139144 * A054654 A154477 A142071
Adjacent sequences: A081573 A081574 A081575 * A081577 A081578 A081579
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 22 2003
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