A334673 a(n) = 23*a(n-1) - a(n-2) + 1 for n > 1, a(0)=0, a(1)=1.

0, 1, 24, 552, 12673, 290928, 6678672, 153318529, 3519647496, 80798573880, 1854847551745, 42580695116256, 977501140122144, 22439945527693057, 515141245996818168, 11825808712399124808, 271478459139183052417, 6232178751488811080784, 143068632825103471805616

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..735

Francesca Arici and Jens Kaad, Gysin sequences and SU(2)-symmetries of C*-algebras, arXiv:2012.11186 [math.OA], 2020.

Index entries for linear recurrences with constant coefficients, signature (24,-24,1).

Formula

a(n) = A004254(n)*A004254(n+1)/5 = A160695(n+1)/5.

G.f.: x/((1-x)*(x^2-23*x+1)). - Alois P. Heinz, Sep 11 2020

From Klaus Purath, Jun 18 2025: (Start)

a(n) = (A004253(n+1)^2 - 1) / 15.

a(n) = (A030221(n)^2 - 1) / 35.

a(n) + a(n+1) = A004253(n+1)^2. (End)

Sum_{n>=1} 1/a(n) = (5/2) * (5 - sqrt(21)). - Amiram Eldar, Jan 29 2026

Mathematica

CoefficientList[Series[x/((1 - x) (x^2 - 23 x + 1)), {x, 0, 18}], x] (* Michael De Vlieger, Apr 07 2021 *)

Crossrefs

Cf. A004253, A004254, A030221, A097778 (first differences), A160695.

Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).

Sequence in context: A362357 A162810 A010561 * A342888 A163174 A163519

Adjacent sequences: A334670 A334671 A334672 * A334674 A334675 A334676

Keyword

nonn,easy

Author

Francesca Arici, Sep 11 2020

Extensions

a(13)-a(14) corrected and more terms added by Alois P. Heinz, Sep 11 2020

Status

approved