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

Offset: 0

Author

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

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A056241, A098158, A145302, A152266.

Programs

Magma

Z:= PolynomialRing(Integers()); N:=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

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

Extensions

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