A164553 a(n) = 14*a(n-1)-43*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

1, 11, 111, 1081, 10361, 98571, 934471, 8844041, 83634321, 790586731, 7471938431, 70611908601, 667273367881, 6305515080491, 59584456307991, 563045239850761, 5320501736667041, 50276078999755851, 475083531319899151

Offset

0,2

Comments

Binomial transform of A164552.

Links

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

Index entries for linear recurrences with constant coefficients, signature (14, -43).

Formula

a(n) = ((3+2*sqrt(6))*(7+sqrt(6))^n+(3-2*sqrt(6))*(7-sqrt(6))^n)/6.

G.f.: (1-3*x)/(1-14*x+43*x^2).

Mathematica

LinearRecurrence[{14, -43}, {1, 11}, 30] (* Harvey P. Dale, Mar 10 2013 *)

Prog

(Magma) [ n le 2 select 10*n-9 else 14*Self(n-1)-43*Self(n-2): n in [1..19] ];
(PARI) a(n)=([0, 1; -43, 14]^n*[1; 11])[1, 1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A164552.

Sequence in context: A267356 A215559 A346231 * A386565 A355280 A282911

Adjacent sequences: A164550 A164551 A164552 * A164554 A164555 A164556

Keyword

nonn,easy

Author

Klaus Brockhaus, Aug 15 2009

Status

approved