OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170767, although the two sequences are eventually different.
Computed with Magma using commands similar to those used to compute A154638.
Which gf is correct? They differ at a(16). - Charles R Greathouse IV, May 18 2026
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,-1081).
FORMULA
G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/( 1081*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
From G. C. Greubel, Jan 17 2023: (Start)
a(n) = Sum_{j=1..15} a(n-j) - 1081*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 47*x + 1127*x^16 - 1081*x^17). (End)
MATHEMATICA
coxG[{16, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2016 *)
(* Alternative: *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-47*t+1127*t^16-1081*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 03 2016; Jan 17 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^16)/(1-47*x+1127*x^16-1081*x^17) )); // G. C. Greubel, Jan 17 2023
(SageMath)
def A167980_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-47*x+1127*x^16-1081*x^17) ).list()
A167980_list(30) # G. C. Greubel, Jan 17 2023
(PARI) Vec((1+x)*(1-x^16)/(1 - 47*x + 1127*x^16 - 1081*x^17)+O(x^30)) \\ Charles R Greathouse IV, May 19 2026
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved
