A143472 Expansion of 1/(1 - x^3 - x^5 - x^7 + x^10), inverse of a Salem polynomial.

1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 3, 3, 4, 5, 6, 7, 9, 11, 14, 17, 20, 26, 31, 38, 48, 58, 72, 88, 108, 134, 164, 202, 249, 306, 376, 463, 570, 701, 863, 1061, 1306, 1607, 1976, 2433, 2993, 3682, 4531, 5574, 6859, 8439, 10383, 12776, 15719, 19340, 23796

Offset

0,9

Comments

The ratio productive positive root is 1.2303914344072246.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1,0,1,0,0,-1).

Formula

G.f.: 1/(1 - x^3 - x^5 - x^7 + x^10). - Colin Barker, Oct 23 2013

a(n) = a(n-3) + a(n-5) + a(n-7) - a(n-10). - Franck Maminirina Ramaharo, Oct 30 2018

Mathematica

CoefficientList[Series[1/(1 - x^3 - x^5 - x^7 + x^10), {x, 0, 50}], x]

Prog

(Maxima) makelist(ratcoef(taylor(1/(1 - x^3 - x^5 - x^7 + x^10), x, 0, n), x, n), n, 0, 50); /* Franck Maminirina Ramaharo, Nov 02 2018 */
(PARI) x='x+O('x^50); Vec(1/(1-x^3-x^5-x^7+x^10)) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^5-x^7+x^10))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A138585 A070048 A116498 * A180235 A239493 A331849

Adjacent sequences: A143469 A143470 A143471 * A143473 A143474 A143475

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Oct 24 2008

Extensions

More terms from Colin Barker, Oct 23 2013

New name after Colin Barker's formula by Franck Maminirina Ramaharo, Nov 03 2018

Status

approved