A143619 - OEIS

A143619

Expansion of 1/(1 - x^2 - x^7 - x^12 + x^14) (a Salem polynomial).

1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 8, 9, 12, 13, 17, 19, 24, 28, 34, 41, 49, 59, 71, 86, 103, 124, 149, 179, 215, 259, 311, 375, 450, 542, 651, 784, 942, 1133, 1363, 1638, 1971, 2369, 2851, 3427, 4123, 4957, 5962, 7170, 8622, 10370, 12470, 14998, 18035, 21691, 26085, 31371

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OFFSET

0,10

COMMENTS

Low growth rate of 1.20262... .The absolute values of the roots of the polynomial are 0.8315201041..., 1.2026167436..., and 1.0 (with multiplicity 12). The polynomial is self-reciprocal. - Joerg Arndt, Nov 03 2012

LINKS

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

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

FORMULA

G.f.: 1/(1 - x^2 - x^7 - x^12 + x^14). - Colin Barker, Nov 03 2012

a(n) = a(n-2) + a(n-7) + a(n-12) - a(n-14). - Franck Maminirina Ramaharo, Nov 02 2018

MATHEMATICA

CoefficientList[Series[1/(1 - x^2 - x^7 - x^12 + x^14), {x, 0, 50}], x]

LinearRecurrence[{0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1}, {1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 4}, 70] (* Harvey P. Dale, Aug 08 2022 *)

PROG

(PARI) x='x+O('x^50); Vec(1/(1-x^2-x^7-x^12+x^14)) \\ G. C. Greubel, Nov 03 2018

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x^2-x^7-x^12+x^14))); // G. C. Greubel, Nov 03 2018

CROSSREFS

Cf. A029826, A117791, A143419, A143438, A143472, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A054685 A286220 A246581 * A029141 A257880 A240866

Adjacent sequences: A143616 A143617 A143618 * A143620 A143621 A143622

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 26 2008

EXTENSIONS

New name from Colin Barker and Joerg Arndt, Nov 03 2012

STATUS

approved