A152266 a(n) = ((9 + sqrt(7))^n + (9 - sqrt(7))^n)/2.

1, 9, 88, 918, 10012, 112284, 1280224, 14735016, 170493712, 1978495632, 22996386688, 267526283616, 3113740490176, 36250383835584, 422090112767488, 4915093625981568, 57237016922874112, 666549376289097984

Offset: 0

Author

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

Keywords

• nonn

Comments

Binomial transform of A152265. - Philippe Deléham, Dec 03 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (18, -74).

Crossrefs

Cf. A098158, A152265.

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-7); S:=[ ((9+r7)^n+(9-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) = 18*a(n-1) - 74*a(n-2), n > 1; a(0)=1, a(1)=9.

G.f.: (1-9*x)/(1-18*x+74*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*7^(n-k). (End)

Extensions

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