OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (24,-179,396).
FORMULA
a(n) = 4^(n+2)/35 +11^(n+2)/14 -9^(n+2)/10. - R. J. Mathar, Nov 11 2012
a(0)=1, a(1)=24, a(2)=397; for n>2, a(n) = 24*a(n-1) -179*a(n-2) +396*a(n-3). - Vincenzo Librandi, Jul 03 2013
a(n) = 20*a(n-1) -99*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013
MAPLE
a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [24, -179, 396][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # Alois P. Heinz, Jul 03 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 4 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{24, -179, 396}, {1, 24, 397}, 20] (* Harvey P. Dale, Nov 16 2021 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 24, 397]; [n le 3 select I[n] else 24*Self(n-1)-179*Self(n-2)+396*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved