OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (16,-81,126).
FORMULA
a(0)=1, a(1)=16, a(2)=175; for n>2, a(n) = 16*a(n-1) -81*a(n-2) +126*a(n-3). - Vincenzo Librandi, Jul 02 2013
a(n) = 13*a(n-1) -42*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013
a(n) = (3*7^(n+2) - 4*6^(n+2) + 3^(n+2))/12. - Yahia Kahloune, Jul 06 2013
MAPLE
a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [16, -81, 126][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # Alois P. Heinz, Jul 02 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-7*x)))); // Vincenzo Librandi, Jul 02 2013
(Magma) I:=[1, 16, 175]; [n le 3 select I[n] else 16*Self(n-1)-81*Self(n-2)+126*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved