A022029 a(n) = 3*a(n-1) + a(n-2) - a(n-3) - a(n-5).

4, 13, 42, 135, 433, 1388, 4449, 14260, 45706, 146496, 469546, 1504979, 4823727, 15460908, 49554976, 158832563, 509086778, 1631714194, 5229935889, 16762880107, 53728029453, 172207945799, 551957272549, 1769121798104, 5670351840955, 18174492018967

Offset

0,1

Comments

Sequence agrees with A010919 for n <= 35 only.

a(36) = 6665569973023362368 and A010919(36) = 6665569973023362367. - Zhuorui He, Nov 08 2025

Links

Zhuorui He, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,1,-1,0,-1).

Formula

G.f.: (4+x-x^2-x^4)/(1-3*x-x^2+x^3+x^5). - R. J. Mathar, Oct 25 2008

Mathematica

LinearRecurrence[{3, 1, -1, 0, -1}, {4, 13, 42, 135, 433}, 30] (* Paolo Xausa, May 29 2026 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -1, 0, -1, 1, 3]^n*[4; 13; 42; 135; 433])[1, 1] \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A010919.

Sequence in context: A192910 A289807 A010919 * A389173 A277667 A274952

Adjacent sequences: A022026 A022027 A022028 * A022030 A022031 A022032

Keyword

nonn,easy,changed

Author

R. K. Guy

Extensions

More terms from Zhuorui He, Nov 08 2025

Status

approved