OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,-378).
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)/( 378*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
From G. C. Greubel, Sep 07 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 28*t + 405*t^16 - 378*t^17).
a(n) = 27*Sum_{j=1..15} a(n-j) - 378*a(n-16). (End)
MATHEMATICA
coxG[{16, 378, -27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 16 2016 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-28*t+405*t^16-378*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 07 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-28*x+405*x^16-378*x^17) )); // G. C. Greubel, Sep 07 2023
(SageMath)
def A167944_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-28*x+405*x^16-378*x^17) ).list()
A167944_list(40) # G. C. Greubel, Sep 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved