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Search: id:A099365
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| 0, 1, 25, 676, 18225, 491401, 13249600, 357247801, 9632441025, 259718659876, 7002771375625, 188815108482001, 5091005157638400, 137268324147754801, 3701153746831741225, 99793882840309258276, 2690733682941518232225
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OFFSET
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0,3
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COMMENT
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See the comment in A099279. This is example a=5.
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= A052918(n-1)^2, n>=1, a(0):=0.
a(n)= 26*a(n-1) + 26*a(n-2) - a(n-3), n>=3; a(0)=0, a(1)=1, a(2)=25.
a(n)= 27*a(n-1) - a(n-2) - 2*(-1)^n, n>=2; a(0)=0, a(1)=1.
a(n)= 2*(T(n, 27/2)-(-1)^n)/29 with twice the Chebyshev's T(n, x) polynomials of the first kind. 2*T(n, 27/2)=A090248(n).
G.f.: x*(1-x)/((1-27*x+x^2)*(1+x)) = x*(1-x)/(1-26*x-26*x^2+x^3).
a(n)=-(2/29)*(-1)^n+(1/29)*[27/2-(5/2)*sqrt(29)]^n+(1/29)*[27/2+(5/2)*sqrt(29)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 27 2008]
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MAPLE
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with (combinat):seq(fibonacci(n, 5)^2, n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 09 2008
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CROSSREFS
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Cf. A007598, A079291, A092936, A099279, A099366 (other square sequences of this type).
Adjacent sequences: A099362 A099363 A099364 this_sequence A099366 A099367 A099368
Sequence in context: A042202 A097194 A015697 this_sequence A123835 A012835 A132540
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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