A302330 a(0)=1, a(1)=97; for n>1, a(n) = 98*a(n-1) - a(n-2).

1, 97, 9505, 931393, 91267009, 8943235489, 876345810913, 85872946233985, 8414672385119617, 824552020795488481, 80797683365572751521, 7917348417805334160577, 775819347261557174985025, 76022378683214797814371873, 7449417291607788628633458529

Offset: 0

Author

Bruno Berselli, Apr 05 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..500
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (98,-1).

Crossrefs

Fifth row of the array A188646.

First bisection of A041275, A042151.

Similar sequences of the type cosh((2*n+1)*arccosh(k))/k are listed in A302329.

Programs

Mathematica

LinearRecurrence[{98, -1}, {1, 97}, 20]

PARI

x='x+O('x^99); Vec((1-x)/(1-98*x+x^2)) \\ Altug Alkan, Apr 06 2018

Formula

G.f.: (1 - x)/(1 - 98*x + x^2).

a(n) = a(-1-n).

a(n) = cosh((2*n + 1)*arccosh(5))/5.

a(n) = ((5 + 2*sqrt(6))^(2*n + 1) + 1/(5 + 2*sqrt(6))^(2*n + 1))/10.

a(n) = (1/5)*T(2*n+1, 5), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Jul 08 2022