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,-119,269,-168).
FORMULA
a(n) = (3*8^(n+4)-5*7^(n+4)+7*3^(n+4)-10)/840. - Yahia Kahloune, May 24 2013
a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1) -56*a(n-2) +(3^n - 1)/2. - Vincenzo Librandi, Jul 11 2013
a(0)=1, a(1)=19, a(2)=242, a(3)=2606; for n>3, a(n) = 19*a(n-1) -119*a(n-2) +269*a(n-3) -168*a(n-4). - Vincenzo Librandi, Jul 11 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 -x) (1 - 3 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{19, -119, 269, -168}, {1, 19, 242, 2606}, 30] (* Harvey P. Dale, Jan 10 2016 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 19, 242, 2606]; [n le 4 select I[n] else 19*Self(n-1)-119*Self(n-2)+269*Self(n-3)-168*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved