A152264 a(n) = ((9+sqrt(6))^n + (9-sqrt(6))^n)/2.

1, 9, 87, 891, 9513, 104409, 1165887, 13155291, 149353713, 1701720009, 19429431687, 222100769691, 2540606477913, 29073358875609, 332774973917487, 3809447614844091, 43611934023382113, 499306241307571209

Offset: 0

Author

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

Keywords

• nonn

Comments

Binomial transform of A152263. - Philippe Deléham, Dec 03 2008

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..944
• Index entries for linear recurrences with constant coefficients, signature (18, -75).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-6); S:=[ ((9+r6)^n+(9-r6)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008

Mathematica

CoefficientList[Series[(1-9x)/(1-18x+75x^2),{x,0,20}],x] (* or *) LinearRecurrence[{18,-75},{1,9},20] (* Harvey P. Dale, Feb 07 2023 *)

Formula

From Philippe Deléham, Dec 03 2008: (Start)

a(n) = 18*a(n-1) - 75*a(n-2), n > 1; a(0)=1, a(1)=9.

G.f.: (1-9*x)/(1-18*x+75*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*6^(n-k). (End)

Extensions

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