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Search: id:A117715
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| A117715 |
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Triangle T(n,m) containing the value of the Fibonacci polynomial F(n,x) at x=m. |
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3
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| 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)
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OFFSET
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0,6
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REFERENCES
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Steven Wolfram, The Mathematica Book, Cambridge University Press, 3rd ed. 1996, page 728
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LINKS
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Eric W. Weisstein, Fibonacci Polynomial, MathWorld.
Wikipedia, Fibonacci Polynomial
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FORMULA
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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]
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EXAMPLE
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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;
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MAPLE
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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
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MATHEMATICA
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a = Table[Table[Fibonacci[n, m], {m, 0, n}], {n, 0, 10}] Flatten[a]
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CROSSREFS
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Cf. A000045, A117716, A049310, A073133, A157103 (antidiagonals).
Adjacent sequences: A117712 A117713 A117714 this_sequence A117716 A117717 A117718
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 13 2006
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EXTENSIONS
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Definition simplified by the Assoc. Edts. of the OEIS, Nov 17 2009.
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