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A099397 Chebyshev's polynomial of the first kind, T(n,x), evaluated at x=51. 4
1, 51, 5201, 530451, 54100801, 5517751251, 562756526801, 57395647982451, 5853793337683201, 597029524795704051, 60891157735824130001, 6210301059529265556051, 633389816914249262587201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used in A099374.

Numbers n such that 26*(n^2-1) is square. [From Vincenzo Librandi, Nov 17 2010]

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..497

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (102, -1).

FORMULA

a(n) = 102*a(n-1) - a(n-2), n>=1; a(-1):= 51, a(0)=1.

a(n) = T(n, 51) = (S(n, 102)-S(n-2, 102))/2 = S(n, 102)-51*S(n-1, 102) with T(n, x), resp. S(n, x), Chebyshev's polynomials of the first, resp.second, kind. See A053120 and A049310. S(n, 102)=(n).

a(n) = (ap^n + am^n)/2 with ap := 51+10*sqrt(26) and am := 51-10*sqrt(26).

a(n) = sum(((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*51)^(n-2*k), k=0..floor(n/2)), n>=1. a(0):=1.

G.f.: (1-51*x)/(1-102*x+x^2).

MATHEMATICA

LinearRecurrence[{102, -1}, {1, 51}, 13] (* Ray Chandler, Aug 11 2015 *)

PROG

(MAGMA) [n: n in [1..1000] |IsSquare(26*(n^2-1))] // Vincenzo Librandi, Nov 17 2010

CROSSREFS

Row 5 of array A188645.

Sequence in context: A172868 A015271 A221116 * A093251 A184282 A232278

Adjacent sequences:  A099394 A099395 A099396 * A099398 A099399 A099400

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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Last modified March 26 18:46 EDT 2017. Contains 284137 sequences.