A350919 - OEIS

A350919

a(0) = 9, a(1) = 9, and a(n) = 3*a(n-1) - a(n-2) - 4 for n >= 2.

9, 9, 14, 29, 69, 174, 449, 1169, 3054, 7989, 20909, 54734, 143289, 375129, 982094, 2571149, 6731349, 17622894, 46137329, 120789089, 316229934, 827900709, 2167472189, 5674515854, 14856075369, 38893710249, 101825055374, 266581455869, 697919312229, 1827176480814, 4783610130209, 12523653909809, 32787351599214, 85838400887829, 224727851064269

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OFFSET

0,1

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

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

FORMULA

a(n) = 5*A032908(n) - 1. - Hugo Pfoertner, Jan 22 2022

G.f.: (3 - 2*x)*(3 - 7*x)/((1 - x)*(1 - 3*x + x^2)). - Stefano Spezia, Jan 22 2022

a(n) = 5*A001519(n) +4. - R. J. Mathar, Feb 07 2022

MATHEMATICA

nxt[{a_, b_}]:={b, 3b-a-4}; NestList[nxt, {9, 9}, 40][[;; , 1]] (* or *) LinearRecurrence[{4, -4, 1}, {9, 9, 14}, 40] (* Harvey P. Dale, Jul 19 2024 *)

CROSSREFS

Cf. A032908, A350916.

Other sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4: A103974, A350917, A350920, A350921, A350922, A350923, A350924, A350925, A350926.

Sequence in context: A175219 A124475 A179057 * A144418 A003885 A344335

Adjacent sequences: A350916 A350917 A350918 * A350920 A350921 A350922

KEYWORD

nonn,easy

AUTHOR

Max Alekseyev, Jan 22 2022

STATUS

approved