OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..685
Index entries for linear recurrences with constant coefficients, signature (27, 27, 27, -378).
FORMULA
G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 27*(a(n-1) + a(n-2) + a(n-3) -14*a(n-4)).
G.f.: (1+x)*(1-x^4)/(1 - 28*x + 405*x^4 - 378*x^5). (End)
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(378*t^4-27*t^3-27*t^2 - 27*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{27, 27, 27, -378}, {1, 29, 812, 22736, 636202}, 20] (* G. C. Greubel, Dec 10 2016 *)
coxG[{4, 378, -27}] (* 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)/(1-28*x+405*x^4-378*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[29, 812, 22736, 636202];; for n in [5..20] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3] -14*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