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A020978
Expansion of 1/((1-8*x)*(1-9*x)*(1-12*x)).
1
1, 29, 565, 9245, 137221, 1915949, 25677205, 334395965, 4265954341, 53604494669, 666045061045, 8206250792285, 100467119521861, 1224084180206189, 14859716922480085, 179888148281902205
OFFSET
0,2
FORMULA
a(n) = (12^(n+2) - 4*9^(n+2) + 3*8^(n+2))/12. - Yahia Kahloune, Jun 30 2013
a(0)=1, a(1)=29, a(2)=565; for n>2, a(n) = 29*a(n-1) -276*a(n-2) +864*a(n-3). - Vincenzo Librandi, Jul 05 2013
a(n) = 21*a(n-1) -108*a(n-2) +8^n. - Vincenzo Librandi, Jul 05 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 8 x) (1 - 9 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)
LinearRecurrence[{29, -276, 864}, {1, 29, 565}, 16] (* Robert G. Wilson v, Jul 05 2013 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-12*x)))); /* or */ I:=[1, 29, 565]; [n le 3 select I[n] else 29*Self(n-1)-276*Self(n-2)+864*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 05 2013
(PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-9*x)*(1-12*x))) \\ G. C. Greubel, Feb 09 2018
CROSSREFS
Sequence in context: A024435 A020979 A025985 * A023948 A020974 A167740
KEYWORD
nonn,easy
STATUS
approved