OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..995
Index entries for linear recurrences with constant coefficients, signature (9,9,9,-45).
FORMULA
G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 9*(a(n-1) + a(n-2) + a(n-3) - 5*a(n-4)).
G.f.: (1+x)*(1-x^4)/(1 - 10*x + 54*x^4 - 45*x^5). (End)
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5), {x, 0, 20}], x] (* or *) coxG[{4, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)) \\ G. C. Greubel, Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[11, 110, 1100, 10945];; for n in [5..20] do a[n]:=9*(a[n-1]+a[n-2] +a[n-3] -5*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved