A274039 Expansion of (x^4 + x^10) / (1 - 2*x + x^2).

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, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112

Offset: 0

Author

Sean A. Irvine, Jun 07 2016

Keywords

• nonn
• easy

Comments

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

Links

• Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
• Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A004279, A005377.

Programs

Mathematica

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

Formula

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

a(n) = 2*(n-6), n>=9. - R. J. Mathar, Jun 09 2016

a(n) = A004279(n-4) for n >= 4. - Georg Fischer, Oct 30 2018