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Search: id:A092886
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| A092886 |
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Expansion of x/(x^4-x^3-2x^2-x+1). |
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+0
4
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| 0, 1, 1, 3, 6, 12, 26, 53, 111, 231, 480, 1000, 2080, 4329, 9009, 18747, 39014, 81188, 168954, 351597, 731679, 1522639, 3168640, 6594000, 13722240, 28556241, 59426081, 123666803, 257352966, 535556412, 1114503066, 2319302053
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OFFSET
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0,4
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COMMENT
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If P(x),Q(x) are n-th and (n-1)-th Fibonacci polynomials, then a(n)=real part of the product of P(I) and conjugate Q(I).
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FORMULA
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G.f.: x/(x^4-x^3-2x^2-x+1). a(n)=a(n-1)+2*a(n-2)+a(n-3)-a(n-4). a(n)=-a(-2-n).
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EXAMPLE
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Fibonacci polynomials P(5)=1+4x+3x^2, P(4)=1+3x+x^2. Conjugate product evaluated at I is (-2+4I)*(-3I)=12-6I and so a(5)=12.
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PROGRAM
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(PARI) a(n)=local(m); if(n<1, if(n>-3, 0, -a(-2-n)), m=contfracpnqn(matrix(2, n, i, j, I)); real(m[1, 1]*conj(m[2, 1])))
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CROSSREFS
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Sequence in context: A077854 A099445 A004067 this_sequence A135035 A054195 A054190
Adjacent sequences: A092883 A092884 A092885 this_sequence A092887 A092888 A092889
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 11 2004
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