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A147961
a(n) = ((6+sqrt(3))^n + (6-sqrt(3))^n)/2.
2
1, 6, 39, 270, 1953, 14526, 109863, 838998, 6442497, 49623030, 382873959, 2956927518, 22848289569, 176600866734, 1365216845031, 10554773538150, 81605126571777, 630953992102374, 4878478728359847, 37720263000939822
OFFSET
0,2
FORMULA
From Philippe Deléham, Nov 19 2008: (Start)
a(n) = 12*a(n-1) - 33*a(n-2) for n > 1, with a(0)=1, a(1)=6.
G.f.: (1-6x)/(1-12x+33x^2).
a(n) = (Sum_{k=0..n} A098158(n,k)*6^(2k)*3^(n-k))/6^n. (End)
EXAMPLE
a(3)=270
MATHEMATICA
CoefficientList[Series[(1-6x)/(1-12x+33x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, -33}, {1, 6}, 30] (* Harvey P. Dale, Jul 30 2021 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((6+r3)^n+(6-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 19 2008
CROSSREFS
Sequence in context: A357206 A370026 A199491 * A264232 A372536 A068765
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008
EXTENSIONS
Extended beyond a(6) by Klaus Brockhaus, Nov 19 2008
STATUS
approved