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A225499
Expansion of 1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12).
24
1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 7, 9, 11, 13, 16, 20, 25, 31, 39, 48, 59, 74, 92, 113, 140, 175, 217, 269, 334, 414, 513, 637, 791, 981, 1217, 1510, 1874, 2325, 2884, 3578, 4440, 5509, 6835, 8481, 10522, 13054, 16197, 20097, 24934, 30936, 38384
OFFSET
0,8
COMMENTS
Limiting ratio is 1.24073..., the largest real root of 1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12: 1.240726423652541392056148161575
is a candidate for the smallest degree-12 Salem number.
LINKS
Michael Mossinghoff, Small Salem Numbers
FORMULA
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) + a(n-9) - a(n-10) + a(n-11) - a(n-12). - Franck Maminirina Ramaharo, Nov 02 2018
MATHEMATICA
CoefficientList[Series[1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12), {x, 0, 50}], x]
LinearRecurrence[{1, -1, 1, 0, 0, 1, 0, 0, 1, -1, 1, -1}, {1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4}, 100] (* G. C. Greubel, Nov 16 2016 *)
PROG
(PARI) Vec(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12) + O(x^50)) \\ G. C. Greubel, Nov 16 2016
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12))); // G. C. Greubel, Nov 03 2018
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 09 2013
STATUS
approved