A152055 a(n) = ((8 + sqrt(3))^n + (8 - sqrt(3))^n)/2.

1, 8, 67, 584, 5257, 48488, 455131, 4324328, 41426257, 399036104, 3857575987, 37380013448, 362768079961, 3524108459048, 34256882467147, 333139503472424, 3240562225062817, 31527485889187208, 306765478498163491

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 22 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 (16, -61).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((8+r3)^n+(8-r3)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 2008

Mathematica

LinearRecurrence[{16,-61},{1,8},30] (* Harvey P. Dale, Sep 02 2018 *)

Formula

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 16*a(n-1) - 61*a(n-2), n > 1; a(0)=1, a(1)=8.

G.f.: (1-8*x)/(1-16x+61*x^2).

a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2*k)*3^(n-k))/8^n. (End)

Extensions

Extended beyond a(6) by Klaus Brockhaus and Philippe Deléham, Nov 26 2008