|
%I #26 Sep 08 2022 08:45:37
%S 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,
%T 59,71,86,103,124,149,179,215,259,311,375,450,542,651,784,942,1133,
%U 1363,1638,1971,2369,2851,3427,4123,4957,5962,7170,8622,10370,12470,14998,18035,21691,26085,31371
%N Expansion of 1/(1 - x^2 - x^7 - x^12 + x^14) (a Salem polynomial).
%C 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
%H G. C. Greubel, <a href="/A143619/b143619.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,1,0,0,0,0,1,0,-1).
%F G.f.: 1/(1 - x^2 - x^7 - x^12 + x^14). - _Colin Barker_, Nov 03 2012
%F a(n) = a(n-2) + a(n-7) + a(n-12) - a(n-14). - _Franck Maminirina Ramaharo_, Nov 02 2018
%t CoefficientList[Series[1/(1 - x^2 - x^7 - x^12 + x^14), {x, 0, 50}], x]
%t 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 *)
%o (PARI) x='x+O('x^50); Vec(1/(1-x^2-x^7-x^12+x^14)) \\ _G. C. Greubel_, Nov 03 2018
%o (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
%Y Cf. A029826, A117791, A143419, A143438, A143472, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K nonn,easy
%O 0,10
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 26 2008
%E New name from _Colin Barker_ and _Joerg Arndt_, Nov 03 2012
|
