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Search: id:A128932
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| A128932 |
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Define the Fibonacci polynomials by F[1]=1, F[2]=x; for n>2, F[n] = x*F[n-1]+F[n-2] (cf. A049310, A053119). Mitrinovic states that F[n] <= G[n] = (x^2+1)^2*(x^2+2)^(n-3) for n >= 3. Sequence gives triangle of coefficients of G[n]-F[n] read by rows. |
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| 0, 0, 1, 0, 1, 2, -2, 5, -1, 4, 0, 1, 3, 0, 9, 0, 12, 0, 6, 0, 1, 8, -3, 28, -4, 38, -1, 25, 0, 8, 0, 1, 15, 0, 58, 0, 99, 0, 87, 0, 41, 0, 10, 0, 1, 32, -4, 144, -10, 272, -6, 280, -1, 170, 0, 61, 0, 12, 0, 1, 63, 0, 310, 0, 673, 0, 825, 0, 619, 0, 292, 0, 85, 0, 14, 0, 1
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OFFSET
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3,6
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REFERENCES
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D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 232, Sect. 3.3.38.
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EXAMPLE
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Triangle begins:
0,0,1,0,1
2,-2,5,-1,4,0,1
3,0,9,0,12,0,6,0,1
8,-3,28,-4,38,-1,25,0,8,0,1
15,0,58,0,99,0,87,0,41,0,10,0,1
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CROSSREFS
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Sequence in context: A073690 A079301 A079300 this_sequence A071950 A068762 A021448
Adjacent sequences: A128929 A128930 A128931 this_sequence A128933 A128934 A128935
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KEYWORD
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sign,tabf
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AUTHOR
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njas, Apr 28 2007
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