OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (45, 45, 45, -1035).
FORMULA
G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)-1035*a(n-4). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3-45*t^2 - 45*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {45, 45, 45, -1035}, {47, 2162, 99452, 4573711}, 20] (* G. C. Greubel, Dec 12 2016 *)
coxG[{4, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3- 45*t^2-45*t+1)) \\ G. C. Greubel, Dec 12 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5) )); // G. C. Greubel, May 01 2019
(Sage) ((1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019
(GAP) a:=[47, 2162, 99452, 4573711];; for n in [5..20] do a[n]:=45*(a[n-1]+a[n-2] +a[n-3]-23*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, May 01 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved