A350921 - OEIS

A350921

a(0) = 3, a(1) = 3, and a(n) = 6*a(n-1) - a(n-2) - 4 for n >= 2.

3, 3, 11, 59, 339, 1971, 11483, 66923, 390051, 2273379, 13250219, 77227931, 450117363, 2623476243, 15290740091, 89120964299, 519435045699, 3027489309891, 17645500813643, 102845515571963, 599427592618131, 3493720040136819, 20362892648202779, 118683635849079851, 691738922446276323

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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

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

FORMULA

G.f.: (3 - 18*x + 11*x^2)/((1 - x)*(1 - 6*x + x^2)). - Stefano Spezia, Jan 22 2022

a(n) = 2*A001653(n) + 1 = 4*A011900(n-1) - 1 for n >= 1. - Hugo Pfoertner, Jan 22 2022

MATHEMATICA

LinearRecurrence[{7, -7, 1}, {3, 3, 11}, 30] (* Harvey P. Dale, Mar 09 2026 *)

CROSSREFS

Cf. A001653, A011900, A350916.

Other sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4: A103974, A350917, A350919, A350920, A350922, A350923, A350924, A350925, A350926.

Sequence in context: A113892 A334283 A365110 * A352857 A352582 A078225

Adjacent sequences: A350918 A350919 A350920 * A350922 A350923 A350924

KEYWORD

nonn,easy

AUTHOR

Max Alekseyev, Jan 22 2022

STATUS

approved