OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003953, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
a(0) = a(1) = 1 (mod 5), a(n) = 0 (mod 5) for n>=2. - G. C. Greubel, Apr 08 2016
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (9,9,9,9,9,9,9,9,9,-45).
FORMULA
G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 22 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11)) \\ G. C. Greubel, Sep 22 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11) )); // G. C. Greubel, Sep 22 2019
(Sage)
def A165796_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-10*t+54*t^10-45*t^11)).list()
A165796_list(20) # G. C. Greubel, Sep 22 2019
(GAP) a:=[11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 10999999945];; for n in [11..20] do a[n]:=9*Sum([1..9], j-> a[n-j]) -45*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved