A147689 a(n) = ((7 + sqrt(8))^n + (7 - sqrt(8))^n)/2.

1, 7, 57, 511, 4817, 46487, 453321, 4440527, 43581217, 428075431, 4206226137, 41336073247, 406249753841, 3992717550647, 39241805801577, 385683861645551, 3790660025173057, 37256202024955207, 366169767317277561

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 10 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14, -41).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-8); S:=[ ((7+r8)^n+(7-r8)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 13 2008

Mathematica

LinearRecurrence[{14,-41},{1,7},20] (* Harvey P. Dale, Sep 11 2020 *)

Formula

From Philippe Deléham, Nov 13 2008: (Start)

a(n) = 14*a(n-1) - 41*a(n-2), a(0)=1, a(1)=7.

G.f.: (1-7x)/(1-14x+41x^2).

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

Extensions

Extended beyond a(6) by Klaus Brockhaus, Nov 13 2008