OFFSET
0,2
COMMENTS
Used in A099374.
Numbers n such that 26*(n^2-1) is square. - Vincenzo Librandi, Nov 17 2010
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..497
Tanya Khovanova, Recursive Sequences
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 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_{k=0..floor(n/2)} (((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*51)^(n-2*k)), 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
(PARI) a(n) = polchebyshev(n, 1, 51); \\ Michel Marcus, Jan 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 18 2004
STATUS
approved