OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (14,-67,126,-72).
FORMULA
a(0)=1, a(1)=14; for n>1, a(n) = 10*a(n-1) -24*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013
a(0)=1, a(1)=14, a(2)=129, a(3)=994; for n>3, a(n) = 14*a(n-1) -67*a(n-2) +126*a(n-3) -72*a(n-4). - Vincenzo Librandi, Jul 09 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 6 x)), {x, 0, 25}], 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)*(1-6*x)))); /* or */ I:=[1, 14, 129, 994]; [n le 4 select I[n] else 14*Self(n-1)-67*Self(n-2)+126*Self(n-3)-72*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved