OFFSET
0,2
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (45,45,45,45,-1035).
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)+45*a(n-4)-1035*a(n-5). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 04 2017 *)
coxG[{5, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 09 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)) \\ G. C. Greubel, Aug 04 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A163803_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)).list()
A163803_list(20) # G. C. Greubel, Aug 09 2019
(GAP) a:=[47, 2162, 99452, 4574792, 210439351];; for n in [6..30] do a[n]:=45*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1035*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved