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,-65,112,-60).
FORMULA
a(0)=1, a(1)=14; for n>1, a(n) = 11*a(n-1) -30*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013
a(0)=1, a(1)=14, a(2)=131, a(3)=1036; for n>2, a(n) = 14*a(n-1) -65*a(n-2) +112*a(n-3) -60*a(n-4). - Vincenzo Librandi, Jul 07 2013
a(n) = (3*6^(n+3) - 5^(n+4) + 5*2^(n+3) - 3)/60. [Yahia Kahloune, Jul 07 2013]
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{14, -65, 112, -60}, {1, 14, 131, 1036}, 20] (* Harvey P. Dale, Dec 23 2023 *)
PROG
(Magma) I:=[1, 14, 131, 1036]; [n le 4 select I[n] else 14*Self(n-1)-65*Self(n-2)+112*Self(n-3)-60*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-6*x)))); // Vincenzo Librandi, Jul 07 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved