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Search: id:A056771
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| A056771 |
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a(n)=a(-n)=34a(n-1)-a(n-2) and a(0)=1. |
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+0
5
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| 1, 17, 577, 19601, 665857, 22619537, 768398401, 26102926097, 886731088897, 30122754096401, 1023286908188737, 34761632124320657, 1180872205318713601, 40114893348711941777, 1362725501650887306817, 46292552162781456490001
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n) = (r^n+1/r^n)/2 with r = 17+sqrt(17^2-1) = 16*A001110(n)+1 = A001541(2n) = (4*A001109(n))^2+1 = 3*A001109(2n-1)-A001109(2n-2) = A001109(2n)-3*A001109(2n-1).
a(n)= T(n, 17) = T(2*n, 3) with T(n, x) Chebyshev's polynomials of the first kind. See A053120. T(n, 3)= A001541(n).
G.f.: (1-17*x)/(1-34*x+x^2).
a(n) = Cosh[2n*ArcSinh[Sqrt[8]]] - Herbert Kociemba (kociemba(AT)t-online.de), Apr 24 2008
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PROGRAM
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sage: [lucas_number2(n, 34, 1)/2 for n in xrange(0, 15)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008
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CROSSREFS
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Cf. A001075, A001541, A001091, A001079, A023038, A011943, A001081, A023039, A001085 and note relationship with square triangular number sequences A001110 and A001109.
Sequence in context: A114063 A112716 A012069 this_sequence A041547 A041544 A009709
Adjacent sequences: A056768 A056769 A056770 this_sequence A056772 A056773 A056774
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KEYWORD
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nonn,easy
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 16 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 07 2000
Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002
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