A350924 a(0) = 1, a(1) = 3, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.

1, 3, 43, 681, 10849, 172899, 2755531, 43915593, 699893953, 11154387651, 177770308459, 2833170547689, 45152958454561, 719614164725283, 11468673677149963, 182779164669674121, 2912997961037635969, 46425188211932501379, 739890013429882386091, 11791815026666185676073

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, A350925, A350926.

Programs

Mathematica

nxt[{a_,b_}]:={b,16b-a-4}; NestList[nxt,{1,3},20][[All,1]] (* or *) LinearRecurrence[ {17,-17,1},{1,3,43},20] (* Harvey P. Dale, Jan 08 2023 *)

Python

a350924 = [1, 3]
for k in range(2, 100): a350924.append(16*a350924[k-1]-a350924[k-2]-4)
print(a350924) # Karl-Heinz Hofmann, Jan 22 2022

Formula

G.f.: (1 - 14*x + 9*x^2)/((1 - x)*(1 - 16*x + x^2)). - Stefano Spezia, Jan 22 2022

7*a(n) = 2 +5*A077412(n) -61*A077412(n-1). - R. J. Mathar, Feb 07 2022