OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (19,-107,221,-132).
FORMULA
a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1) -44*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013
a(0)=1, a(1)=19, a(2)=254, a(3)=3014; for n>3, a(n) = 19*a(n-1) -107*a(n-2) +221*a(n-3) -132*a(n-4). - Vincenzo Librandi, Jul 09 2013
a(n) = (3*11^(n+3) - 80*4^(n+3) + 105*3^(n+3) - 28)/1680. [Yahia Kahloune, Aug 12 2013]
MAPLE
A021394:=n->(3*11^(n+3) - 80*4^(n+3) + 105*3^(n+3) - 28)/1680; seq(A021394(n), n=0..100); # Wesley Ivan Hurt, Nov 11 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 09 2013 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-11*x)))); /* or */ I:=[1, 19, 254, 3014]; [n le 4 select I[n] else 19*Self(n-1)-107*Self(n-2)+221*Self(n-3)-132*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved