A152109 a(n) = ((8+sqrt(5))^n + (8-sqrt(5))^n)/2.

1, 8, 69, 632, 6041, 59368, 593469, 5992792, 60870001, 620345288, 6334194549, 64746740792, 662230374281, 6775628281768, 69338460425709, 709653298187032, 7263483605875681, 74346193100976008, 760993556868950949

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (16, -59).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((8+r5)^n+(8-r5)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 2008

Mathematica

LinearRecurrence[{16,-59},{1,8},30] (* Harvey P. Dale, Dec 18 2011 *)

Formula

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 16*a(n-1) - 59*a(n-2), n > 1; a(0)=1, a(1)=8.

G.f.: (1-8*x)/(1-16*x+59*x^2).

a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2*k)*5^(n-k))/8^n. (End)

Extensions

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