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Search: id:A113859
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| A113859 |
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Expansion of (7-14*x+6*x^2)/((1-x)*(2*x^2-4*x+1)); related to the binomial transform of Pell numbers A000129 (see formula and comment for A007070). |
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| 7, 21, 69, 233, 793, 2705, 9233, 31521, 107617, 367425, 1254465, 4283009, 14623105, 49926401, 170459393, 581984769, 1987020289, 6784111617, 23162405889, 79081400321, 270000789505, 921840357377, 3147359850497, 10745758687233
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OFFSET
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0,1
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COMMENT
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If g.f. (x^6+5*x^4+6*x^2+1)/(x^7+6*x^5+10*x^3+4*x) is expanded, where (x^6+5*x^4+6*x^2+1) and (x^7+6*x^5+10*x^3+4*x) are the 7-th and 8-th Fibonacci polynomials, respectively, the sequence: [0, 7/8, 0, -21/16, 0, 69/32, 0, -233/64, 0, 793/128, 0, -2705/256, ] is returned. (a(n)) is seen to be the numerators of the bisection of this sequences, apart from signs.
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FORMULA
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a(n+1) - a(n) = A007070(n+2), a(n) - 2*a(n+1) + a(n+2) = A007052(n+3) (Number of order consecutive partitions of n), a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n) = A003480(n+4), a(n+2) - a(n) = A111567(n+3)
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MAPLE
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with(combinat, fibonacci): seq(fibonacci(i, x), i=1..15); [[generates sequence of Fibonacci polynomials]]
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CROSSREFS
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Cf. A007070, A007052, A003480, A111567, A000129.
Sequence in context: A083596 A005032 A082541 this_sequence A146533 A135576 A110683
Adjacent sequences: A113856 A113857 A113858 this_sequence A113860 A113861 A113862
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KEYWORD
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easy,nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jan 25 2006
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