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A099366
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Squares of A005668(n) (generalized Fibonacci).
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1
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0, 1, 36, 1369, 51984, 1974025, 74960964, 2846542609, 108093658176, 4104712468081, 155870980128900, 5918992532430121, 224765845252215696, 8535183127051766329, 324112192982714904804, 12307728150216114616225
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OFFSET
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0,3
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COMMENTS
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See the comment in A099279. This is example a=6.
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LINKS
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Table of n, a(n) for n=0..15.
Index entries for linear recurrences with constant coefficients, signature (37, 37, -1).
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n) = A005668(n)^2.
a(n) = 37*a(n-1) + 37*a(n-2) - a(n-3), n >= 3; a(0)=0, a(1)=1, a(2)=36.
a(n) = 38*a(n-1) - a(n-2) - 2*(-1)^n, n >= 2; a(0)=0, a(1)=1.
a(n) = (T(n, 19) - (-1)^n)/20 with the Chebyshev's polynomials of the first kind: T(n, 19) = A078986(n).
G.f.: x*(1-x)/((1 - 38*x + x^2)*(1+x)) = x*(1-x)/(1 - 37*x - 37*x^2 + x^3).
a(n) = -(1/20)*(-1)^n + (1/40)*(19-6*sqrt(10))^n + (1/40)*(19+6*sqrt(10))^n, with n >= 0. - Paolo P. Lava, Aug 27 2008
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MAPLE
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with (combinat):seq(fibonacci(n, 6)^2, n=0..15); # Zerinvary Lajos, Apr 09 2008
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MATHEMATICA
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LinearRecurrence[{37, 37, -1}, {0, 1, 36}, 20] (* Harvey P. Dale, Sep 23 2018 *)
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CROSSREFS
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Sequence in context: A226772 A158739 A218518 * A095657 A209014 A268897
Adjacent sequences: A099363 A099364 A099365 * A099367 A099368 A099369
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Oct 18 2004
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STATUS
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approved
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