A302331 a(0)=1, a(1)=141; for n>1, a(n) = 142*a(n-1) - a(n-2).

1, 141, 20021, 2842841, 403663401, 57317360101, 8138661470941, 1155632611513521, 164091692173449041, 23299864656018250301, 3308416689462418093701, 469771870039007351055241, 66704297128849581431750521, 9471540420426601555957518741, 1344892035403448571364535910701

Offset: 0

Author

Bruno Berselli, Apr 05 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..450
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (142,-1).

Crossrefs

Sixth row of the array A188646.

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

Programs

Mathematica

LinearRecurrence[{142, -1}, {1, 141}, 20]
CoefficientList[Series[(1-x)/(1-142x+x^2),{x,0,20}],x] (* Harvey P. Dale, Jun 21 2021 *)

PARI

x='x+O('x^99); Vec((1-x)/(1-142*x+x^2)) \\ Altug Alkan, Apr 06 2018

Formula

G.f.: (1 - x)/(1 - 142*x + x^2).

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

a(n) = cosh((2*n + 1)*arccosh(6))/6.

a(n) = ((6 + sqrt(35))^(2*n + 1) + 1/(6 + sqrt(35))^(2*n + 1))/12.

a(n) = (1/6)*T(2*n+1, 6), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Jul 08 2022