0,2

The initial terms coincide with those of A170737, although the two sequences are eventually different.

Computed with Magma using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,-136).

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)/( 136*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

From G. C. Greubel, Sep 10 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 17*t + 152*t^16 - 136*t^17).

a(n) = 16*Sum_{j=1..15} a(n-j) - 136*a(n-16). (End)

CoefficientList[Series[(1+t)*(1-t^16)/(1-17*t+152*t^16-136*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)

coxG[{16, 136, -16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 15 2022 *)

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-17*x+152*x^16-136*x^17) )); // G. C. Greubel, Sep 10 2023

(SageMath)

def A167927_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1+x)*(1-x^16)/(1-17*x+152*x^16-136*x^17) ).list()

A167927_list(40) # G. C. Greubel, Sep 10 2023

Cf. A154638, A169452, A170737.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167919, A167922, A167923, A167924, A167926, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

Sequence in context: A167048 A167125 A167674 * A168695 A168743 A168791

Adjacent sequences: A167924 A167925 A167926 * A167928 A167929 A167930

John Cannon and N. J. A. Sloane, Dec 03 2009

approved