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A117715 Triangle T(n,m) containing the value of the Fibonacci polynomial F(n,x) at x=m. 6
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, 6624850, 18674305, 46866034 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

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

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

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, Apr 09 2008

MATHEMATICA

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

PROG

(Python)

from sympy import fibonacci

def T(n, m): return 0 if n==0 else fibonacci(n, m)

for n in range(21): print([T(n, m) for m in range(n + 1)]) # Indranil Ghosh, Aug 12 2017

CROSSREFS

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

Main diagonal and first lower diagonal give: A084844, A084845.

Sequence in context: A199599 A201163 A049901 * A330962 A327194 A160457

Adjacent sequences: A117712 A117713 A117714 * A117716 A117717 A117718

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula, Apr 13 2006

EXTENSIONS

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

STATUS

approved

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Last modified January 30 21:42 EST 2023. Contains 359947 sequences. (Running on oeis4.)