A152265 a(n) = ((8 + sqrt(7))^n + (8 - sqrt(7))^n)/2.

1, 8, 71, 680, 6833, 70568, 739607, 7811336, 82823777, 879934280, 9357993191, 99571637096, 1059740581649, 11280265991912, 120079042716599, 1278289521926600, 13608126915979457, 144867527905855112, 1542217212282852743, 16418026305891902504, 174782039794147833713

Offset

0,2

Comments

Binomial transform of A145302. Inverse binomial transform of A152266. - Philippe Deléham, Dec 03 2008

Links

Paolo Xausa, Table of n, a(n) for n = 0..973

Index entries for linear recurrences with constant coefficients, signature (16,-57).

Formula

From Philippe Deléham, Dec 03 2008: (Start)

a(n) = 16*a(n-1) - 57*a(n-2), n > 1; a(0)=1, a(1)=8.

G.f.: (1-8*x)/(1-16*x+57*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*7^(n-k). (End)

a(n) = Sum_{k=1..n} A056241(n,k) * 7^(k-1). - J. Conrad, Nov 23 2022

Mathematica

LinearRecurrence[{16, -57}, {1, 8}, 25] (* Paolo Xausa, Jul 21 2026 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((8+r7)^n+(8-r7)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008
(PARI) a(n)=([0, 1; -57, 16]^n*[1; 8])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A056241, A098158, A145302, A152266.

Sequence in context: A370178 A187709 A292865 * A081178 A096341 A199687

Adjacent sequences: A152262 A152263 A152264 * A152266 A152267 A152268

Keyword

nonn,easy,changed

Author

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

Extensions

Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008

More terms from Paolo Xausa, Jul 21 2026

Status

approved