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A143419
G.f.: 1/p(x), where p(x) = degree 22 Salem polynomial p(x) = x^22 + x^21 - x^19 - 2*x^18 - 3*x^17 - 3*x^16 - 2*x^15 + 2*x^13 + 4*x^12 + 5*x^11 + 4*x^10 + 2*x^9 - 2*x^7 - 3*x^6 - 3*x^5 - 2*x^4 - x^3 + x + 1.
25
1, -1, 1, 0, 1, 1, 1, 2, 2, 4, 4, 7, 9, 12, 17, 23, 32, 44, 60, 83, 113, 156, 214, 294, 403, 554, 760, 1044, 1433, 1967, 2701, 3708, 5091, 6988, 9596, 13172, 18085, 24828, 34086, 46797, 64246, 88203, 121092, 166246, 228237, 313343, 430185, 590594, 810819
OFFSET
0,8
LINKS
Index entries for linear recurrences with constant coefficients, signature (-1,0,1,2,3,3,2,0,-2,-4,-5,-4,-2,0,2,3,3,2,1,0,-1,-1).
FORMULA
a(n) = -a(n-1) + a(n-3) + 2*a(n-4) + 3*a(n-5) + 3*a(n-6) + 2*a(n-7) - 2*a(n-9) - 4*a(n-10) - 5*a(n-11) - 4*a(n-12) - 2*a(n-13) + 2*a(n-15) + 3*a(n-16) + 3*a(n-17) + 2*a(n-18) + a(n-19) - a(n-21) - a(n-22). - Franck Maminirina Ramaharo, Oct 30 2018
MATHEMATICA
f[x_] = x^22 + x^21 - x^19 - 2*x^18 - 3*x^17 - 3*x^16 - 2*x^15 + 2*x^13 + 4*x^12 + 5*x^11 + 4*x^10 + 2*x^9 - 2*x^7 - 3*x^6 - 3*x^5 - 2*x^4 - x^3 + x + 1;
CoefficientList[Series[1/f[x], {x, 0, 50}], x]
LinearRecurrence[{-1, 0, 1, 2, 3, 3, 2, 0, -2, -4, -5, -4, -2, 0, 2, 3, 3, 2, 1, 0, -1, -1}, {1, -1, 1, 0, 1, 1, 1, 2, 2, 4, 4, 7, 9, 12, 17, 23, 32, 44, 60, 83, 113, 156}, 50] (* Harvey P. Dale, Aug 18 2024 *)
PROG
(PARI) p(x)=x^22 + x^21 - x^19 - 2*x^18 - 3*x^17 - 3*x^16 - 2*x^15 + 2*x^13 + 4*x^12 + 5*x^11 + 4*x^10 + 2*x^9 - 2*x^7 - 3*x^6 - 3*x^5 - 2*x^4 - x^3 + x + 1; Vec(1/p(x)+O(x^60)) \\ Charles R Greathouse IV, Feb 13 2011
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(x^22 +x^21-x^19-2*x^18-3*x^17-3*x^16-2*x^15+2*x^13+4*x^12+5*x^11 + 4*x^10+2*x^9-2*x^7-3*x^6-3*x^5-2*x^4-x^3+x+1))); // G. C. Greubel, Nov 03 2018
KEYWORD
easy,sign
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Dec 12 2008
More terms from Sean A. Irvine, Feb 13 2011
Offset corrected, and more terms from Franck Maminirina Ramaharo, Nov 02 2018
STATUS
approved