A152056 a(n) = ((9+sqrt(3))^n + (9-sqrt(3))^n)/2.

1, 9, 84, 810, 8028, 81324, 837648, 8734392, 91882512, 972602640, 10340011584, 110257202592, 1178108743104, 12605895573696, 135013638364416, 1446985635811200, 15514677652177152, 166399318145915136

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 22 2008

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (18, -78).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((9+r3)^n+(9-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 2008

Formula

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 18*a(n-1) - 78*a(n-2), n > 1; a(0)=1, a(1)=9.

G.f.: (1-9*x)/(1-18*x+78*x^2).

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

Extensions

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