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

0,6

Links

Table of n, a(n) for n=0..41.

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).

Formula

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

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 *)

Prog

(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
(Magma) m:=50; R<x>:=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

Crossrefs

Cf. A013982.

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

Sequence in context: A011981 A238131 A212532 * A187893 A293678 A063984

Adjacent sequences: A109541 A109542 A109543 * A109545 A109546 A109547

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 20 2005

Status

approved