OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,7,7,7,7,-28).
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(28*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
a(n) = -28*a(n-6) + 7*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
coxG[{6, 28, -7}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7)) \\ G. C. Greubel, Aug 13 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163953_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-8*t+35*t^6-28*t^7)).list()
A163953_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[9, 72, 576, 4608, 36864, 294876];; for n in [7..30] do a[n]:=7*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -28*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