OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3).
FORMULA
a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
G.f.: 3*(1 + x + 2*x^2)/(1 - 3*x + x^3 - 3*x^4). - G. C. Greubel, Oct 07 2016 [corrected by Georg Fischer, May 10 2019]
MAPLE
seq(coeff(series(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 21 2019
MATHEMATICA
LinearRecurrence[{3, 0, -1, 3}, {3, 12, 42, 123}, 25] (* G. C. Greubel, Oct 07 2016 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)) \\ G. C. Greubel, Nov 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A135264_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)).list()
A135264_list(30) # G. C. Greubel, Nov 21 2019
(GAP) a:=[3, 12, 42, 123];; for n in [5..30] do a[n]:=3*a[n-1]-a[n-3]+ 3*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019
CROSSREFS
KEYWORD
nonn,less,easy
AUTHOR
Paul Curtz, Dec 02 2007
EXTENSIONS
Edited, corrected and extended by R. J. Mathar, Jul 28 2008
STATUS
approved