login
Expansion of (x^4 + x^10) / (1 - 2*x + x^2).
1

%I #18 Apr 13 2022 13:25:18

%S 0,0,0,0,1,2,3,4,5,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,

%T 40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,

%U 86,88,90,92,94,96,98,100,102,104,106,108,110,112

%N Expansion of (x^4 + x^10) / (1 - 2*x + x^2).

%C This g.f. was incorrectly conjectured by Plouffe in his 1992 disseration to be the g.f. for A005377.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: z^4*(z^2+1)*(z^4-z^2+1)/(z-1)^2. [Simon Plouffe in his 1992 dissertation.]

%F a(n) = 2*(n-6), n>=9. - _R. J. Mathar_, Jun 09 2016

%F a(n) = A004279(n-4) for n >= 4. - _Georg Fischer_, Oct 30 2018

%t CoefficientList[Series[(x^4+x^10)/(1-2x+x^2),{x,0,120}],x] (* _Harvey P. Dale_, Sep 10 2018 *)

%Y Cf. A004279, A005377.

%K nonn,easy

%O 0,6

%A _Sean A. Irvine_, Jun 07 2016