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A081576 Square array of binomial transforms of Fibonacci numbers, read by antidiagonals. 1
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; text; internal format)
OFFSET

0,9

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.

LINKS

Table of n, a(n) for n=0..65.

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)

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 ...

CROSSREFS

Sequence in context: A286223 A008783 A139144 * A292717 A054654 A253669

Adjacent sequences:  A081573 A081574 A081575 * A081577 A081578 A081579

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Mar 22 2003

STATUS

approved

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Last modified March 18 16:27 EDT 2019. Contains 321292 sequences. (Running on oeis4.)