A109544 Expansion of (1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5).

1, 1, 1, 1, 1, 4, 4, 7, 10, 16, 25, 37, 58, 88, 136, 208, 319, 490, 751, 1153, 1768, 2713, 4162, 6385, 9796, 15028, 23056, 35371, 54265, 83251, 127720, 195943, 300607, 461179, 707521, 1085449, 1665250, 2554756, 3919399, 6012976, 9224854, 14152381

Offset: 0

Author

Roger L. Bagula, Jun 20 2005

Keywords

• nonn
• easy

Links

• Peter Borwein and Kevin G. Hare, Some Computations on Pisot and Salem Numbers, CARMA Preprint, 2000, p.7, Table 1.
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,1).

Crossrefs

Cf. A013982.

Cf. A107479, A107480, A109538, A109543, A114749, A125950, A130844, A143335, A147851.

Programs

Magma

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

Mathematica

LinearRecurrence[{0, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, 50]
CoefficientList[Series[(1+x-x^3-2x^4)/(1-x^2-x^3-x^4-x^5),{x,0,50}],x] (* Harvey P. Dale, Oct 24 2021 *)

Maxima

makelist(ratcoef(taylor((1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5), x, 0, n), x, n), n, 0, 50); /* Franck Maminirina Ramaharo, Oct 31 2018 */

PARI

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

Formula

a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5).