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 (9,9,9,9,9,9,-45).
FORMULA
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
a(n) = -45*a(n-7) + 9*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8), {t, 0, 30}], t] (* G. C. Greubel, Aug 12 2017 *)
coxG[{7, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 28 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8)) \\ G. C. Greubel, Aug 12 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8) )); // G. C. Greubel, Aug 28 2019
(Sage)
def A164590_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8)).list()
A164590_list(30) # G. C. Greubel, Aug 28 2019
(GAP) a:=[11, 110, 1100, 11000, 110000, 1100000, 10999945];; for n in [8..30] do a[n]:=9*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -45*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved