OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (23,-160,336).
FORMULA
a(n) = 2*4^n/3 - 7^(n+2)/15 + 18*12^n/5. - R. J. Mathar, Nov 11 2012
a(0)=1, a(1)=23, a(2)=369; for n>2, a(n) = 23*a(n-1) -160*a(n-2) +336*a(n-3). - Vincenzo Librandi, Jul 03 2013
a(n) = 19*a(n-1) - 84*a(n-2) + 4^n. - Vincenzo Librandi, Jul 03 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{23, -160, 336}, {1, 23, 369}, 30] (* G. C. Greubel, Jan 28 2018 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-12*x)))); /* or */ I:=[1, 23, 369]; [n le 3 select I[n] else 23*Self(n-1)-160*Self(n-2)+336*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
(PARI) x='x+O('x^30); Vec(1/((1-4*x)*(1-7*x)*(1-12*x))) \\ G. C. Greubel, Jan 28 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved