A350925 a(0) = 1, a(1) = 9, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.

1, 9, 139, 2211, 35233, 561513, 8948971, 142622019, 2273003329, 36225431241, 577333896523, 9201116913123, 146640536713441, 2337047470501929, 37246118991317419, 593600856390576771, 9460367583257910913, 150772280475735997833, 2402896120028518054411

Offset: 0

Author

Max Alekseyev, Jan 22 2022

Keywords

• nonn
• easy

Comments

One of 10 linear second-order recurrence sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4 and together forming A350916.

Links

• Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

Crossrefs

Cf. A350916.

Other sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4: A103974, A350917, A350919, A350920, A350921, A350922, A350923, A350924, A350926.

Programs

Mathematica

LinearRecurrence[{17,-17,1},{1,9,139},20] (* Harvey P. Dale, Feb 09 2025 *)

Formula

G.f.: (1 - 8*x + 3*x^2)/((1 - x)*(1 - 16*x + x^2)). - Stefano Spezia, Jan 22 2022

7*a(n) = 2+5*A077412(n)-19*A077412(n-1). - R. J. Mathar, Feb 07 2022