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A173911
Expansion of 1/(1 - x + x^2 - x^3 - x^6 + x^7 - x^8 + x^9 - x^10 + x^11 - x^12 -x^15 + x^16 - x^17 + x^18).
24
1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 23, 28, 33, 39, 46, 55, 66, 78, 92, 110, 131, 155, 184, 219, 260, 309, 368, 437, 519, 617, 733, 871, 1036, 1231, 1462, 1737, 2065, 2454, 2916, 3465, 4118, 4894, 5816, 6911, 8213
OFFSET
0,11
COMMENTS
Limiting ratio is 1.188368147508223588... = A219300.
LINKS
Michael Mossinghoff, Small Salem Numbers
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,0,0,1,-1,1,-1,1,-1,1,0,0,1,-1,1,-1).
FORMULA
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) - a(n-7) + a(n-8) - a(n-9) + a(n-10) - a(n-11) + a(n-12) + a(n-15) - a(n-16) + a(n-17) - a(n-16). - Franck Maminirina Ramaharo, Nov 02 2018
MAPLE
seq(coeff(series(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 15 2019
MATHEMATICA
CoefficientList[Series[1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18), {x, 0, 50}], x]
LinearRecurrence[{1, -1, 1, 0, 0, 1, -1, 1, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1}, {1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6}, 60] (* Harvey P. Dale, Apr 02 2024 *)
PROG
(PARI) my(x='x+O('x^50)); Vec(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+ x^16-x^17+x^18)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16-x^17+x^18))); // G. C. Greubel, Nov 03 2018
(Sage)
def A173911_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18) ).list()
A173911_list(50) # G. C. Greubel, Dec 15 2019
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 26 2010
STATUS
approved