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Search: id:A157929
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| A157929 |
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Coefficients of first factor modulo 2 of the near doubled P48q lattice polynomial: (x^97+1)=(x+1)*f1(x)*f2(x); f1(x). |
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+0
1
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| 1, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 1, 2, 1, 3, 0, 1, -1, -2, -5, -2, -6, -3, 0, 0, 5, 10, 10, 7, 14, -1, -1, -12, -17, -29, -18, -27, -10, 8, 20, 45, 57, 62, 47, 48, -26, -36, -102, -129, -162
(list; graph; listen)
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OFFSET
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0,14
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COMMENT
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f1(x)=1 + x^5 + x^7 + x^8 + x^10 + x^12 + x^16 + x^19 + x^24 + x^29 + x^32 + x^36 + x^38 + x^40 + x^41 + x^43 + x^48;
f2(x)=(1 + x + x^2 + x^3 + x^4 + x^7 + x^12 + x^13 + x^15 + x^16 +x^18 + x^19 + x^23 + x^24 + x^25 + x^29 + x^30 + x^32 +x^33 + x^35 + x^36 + x^41 + x^44 + x^45 + x^46 + x^47 +x^48)
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, pp. 231-232 ( also Chap'7. Example 9)
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FORMULA
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The other one mentioned by Sloane and Conway in "Sphere Packings":
Factor[PolynomialMod[(x^97 + 1)/((x + 1)), 2], Modulus -> 2]
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MATHEMATICA
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f[x_] = FactorList[PolynomialMod[(x^97 + 1)/((x + 1)), 2], Modulus -> 2][[2]][[1]];
g[x] = ExpandAll[x^48*f[1/x]];
a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
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CROSSREFS
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Sequence in context: A143255 A127139 A166139 this_sequence A071431 A140699 A140256
Adjacent sequences: A157926 A157927 A157928 this_sequence A157930 A157931 A157932
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 09 2009
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