OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..680
Index entries for linear recurrences with constant coefficients, signature (28,28,28,28,28,-406).
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(406*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
a(n) = -406*a(n-6) + 28*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-29*t+434*t^6-406*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-29*t+434*t^6-406*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)
coxG[{6, 406, -28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 05 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-29*t+434*t^6-406*t^7)) \\ G. C. Greubel, Sep 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-29*t+434*t^6-406*t^7) )); // G. C. Greubel, Aug 10 2019
(SageMath)
def A164027_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-29*t+434*t^6-406*t^7)).list()
A164027_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[30, 870, 25230, 731670, 21218430, 615334035];; for n in [7..30] do a[n]:=28*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -406*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved