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A117715 Triangle T(n,m) containing the value of the Fibonacci polynomial F(n,x) at x=m. +0
3
0, 1, 1, 0, 1, 2, 1, 2, 5, 10, 0, 3, 12, 33, 72, 1, 5, 29, 109, 305, 701, 0, 8, 70, 360, 1292, 3640, 8658, 1, 13, 169, 1189, 5473, 18901, 53353, 129949, 0, 21, 408, 3927, 23184, 98145, 328776, 927843, 2298912, 1, 34, 985, 12970, 98209, 509626, 2026009 (list; table; graph; listen)
OFFSET

0,6

REFERENCES

Steven Wolfram, The Mathematica Book, Cambridge University Press, 3rd ed. 1996, page 728

LINKS

Eric W. Weisstein, Fibonacci Polynomial, MathWorld.

Wikipedia, Fibonacci Polynomial

FORMULA

T(n,1) = A000045(n). T(n,3)=A006190(n). T(n,4) = A001076(n). T(n,5) = A052918(n-1). [Nov 17, 2009]

T(5,m) = A057721(m). T(6,m) = A124152(m). [Nov 17, 2009]

EXAMPLE

0;

1, 1;

0, 1, 2;

1, 2, 5, 10;

0, 3, 12, 33, 72;

1, 5, 29, 109, 305, 701;

0, 8, 70, 360, 1292, 3640, 8658;

1, 13, 169, 1189, 5473, 18901, 53353, 129949;

MAPLE

with(combinat):for n from 0 to 9 do seq(fibonacci(n, m), m = 0 .. n) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 09 2008

MATHEMATICA

a = Table[Table[Fibonacci[n, m], {m, 0, n}], {n, 0, 10}] Flatten[a]

CROSSREFS

Cf. A000045, A117716, A049310, A073133, A157103 (antidiagonals).

Adjacent sequences: A117712 A117713 A117714 this_sequence A117716 A117717 A117718

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 13 2006

EXTENSIONS

Definition simplified by the Assoc. Edts. of the OEIS, Nov 17 2009.

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Last modified December 16 17:18 EST 2009. Contains 170825 sequences.


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