OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (21,-149,399,-270).
FORMULA
a(0)=1, a(1)=21, a(2)=292, a(3)=3402; for n>3, a(n) = 21*a(n-1) -149*a(n-2) +399*a(n-3) -270*a(n-4). - Vincenzo Librandi, Jul 12 2013
a(n) = (5*9^(n+3) - 32*6^(n+3) + 30*5^(n+3) - 3)/480. [Yahia Kahloune, Aug 13 2013]
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 6 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
PROG
(Magma) I:=[1, 21, 292, 3402]; [n le 4 select I[n] else 21*Self(n-1)-149*Self(n-2)+399*Self(n-3)-270*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-6*x)*(1-9*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) a(n) = (5*9^(n+3) - 32*6^(n+3) + 30*5^(n+3) - 3)/480; \\ Joerg Arndt, Aug 13 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved