OFFSET
0,2
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).
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)
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 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r6>:=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
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008
EXTENSIONS
Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008
STATUS
approved