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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| See the comment in A099279. This is example a=6.
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| 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 [From Paolo P. Lava (paoloplava(AT)gmail.com), Aug 27 2008]
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MAPLE
| with (combinat):seq(fibonacci(n, 6)^2, n=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 09 2008
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CROSSREFS
| Sequence in context: A041613 A203333 A158739 * A095657 A034996 A166770
Adjacent sequences: A099363 A099364 A099365 * A099367 A099368 A099369
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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