A147851 Expansion of 1/(1 - x^3 - x^4 - x^5 + x^8)^2.

1, 0, 0, 2, 2, 2, 3, 6, 7, 10, 15, 18, 27, 38, 50, 66, 92, 126, 165, 224, 300, 400, 536, 714, 948, 1258, 1676, 2218, 2932, 3882, 5128, 6768, 8924, 11760, 15479, 20366, 26780, 35174, 46182, 60602, 79473, 104158, 136445, 178654, 233797, 305834, 399881

Offset: 0

Author

Roger L. Bagula, Nov 15 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Roger L. Bagula, Base Polynomial Mathematica Program
• Michael Mossinghoff, Small Salem Numbers
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,2,2,-1,-2,-5,-2,-1,2,2,2,0,0,-1).

Crossrefs

Cf. A107479, A107480, A109538, A109543, A109544, A114749, A125950, A130844, A143335.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x^3-x^4-x^5+x^8)^2)); // G. C. Greubel, Nov 03 2018

Mathematica

CoefficientList[Series[1/(1 - x^3 - x^4 - x^5 + x^8)^2, {x, 0, 50}], x]

PARI

x='x+O('x^50); Vec(1/(1-x^3-x^4-x^5+x^8)^2) \\ G. C. Greubel, Nov 03 2018

Formula

a(n) = 2*a(n-3) + 2*a(n-4) + 2*a(n-5) - a(n-6) - 2*a(n-7) - 5*a(n-8) - 2*a(n-9) - a(n-10) + 2*a(n-11) + 2*a(n-12) + 2*a(n-13) - a(n-16). - Franck Maminirina Ramaharo, Nov 02 2018

Extensions

Name clarified by Franck Maminirina Ramaharo, Nov 02 2018