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Search: id:A117938
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| A117938 |
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Triangle, columns generated from Lucas Polynomials. |
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+0
4
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| 1, 1, 1, 1, 2, 3, 1, 3, 6, 4, 1, 4, 11, 14, 7, 1, 5, 18, 36, 34, 11, 1, 6, 27, 76, 119, 82, 18, 1, 7, 38, 140, 322, 393, 198, 29, 1, 8, 51, 234, 727, 1364, 1298, 478, 47, 1, 9, 66, 364, 1442, 3665, 3778, 4287, 1154, 76
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Companion triangle using Fibonacci polynomial generators = A073133. Inverse binomial transforms of triangle A117938 columns = rows of A117937.
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FORMULA
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Columns are f(x), x = 1,2,3..., of the Lucas Polynomials: (1); (x); (x^2 + 2); (x^3 + 3x); (x^4 + 4x^2 + 2); (x^5 + 5x^3 + 5x); (x^6 + 6x^4 + 9x^2 + 2); (x^7 + 7x^5 + 14x^3 + 7x);...
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 2, 3;
1, 3, 6, 4;
1, 4, 11, 14, 7;
1, 5, 18, 36, 34, 11;
1, 6, 27, 76, 119, 82, 18;
1, 7, 38, 140, 322, 393, 198, 29;
...
For example, T(7,4) = 76 = f(4), x^3 + 3x = 64 + 12 = 76.
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CROSSREFS
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Cf. A073133, A117936, A117937, A117938.
Sequence in context: A020501 A086404 A118981 this_sequence A101912 A111808 A081422
Adjacent sequences: A117935 A117936 A117937 this_sequence A117939 A117940 A117941
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 03 2006
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