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Search: id:A147851
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| A147851 |
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Coefficient expansion of : 1/(1 - x^3 - x^4 - x^5 + x^8)^2= 1/(-1+ 2 x^3 + 2 x^4 + 2 x^5 - x^6 - 2 x^7 - 5x^8 - 2 x^9 - x^10 + 2 x^11 + 2 x^12 + 2 x^13 - x^16) |
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+0
2
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| 1, 0, 0, 2, 2, 2, 3, 6, 7, 10, 15, 18, 27, 38, 50, 66, 92, 126, 165, 224, 300, 400, 536, 714, 948, 1258, 1676, 2218, 2932, 3882, 5128, 6768, 8924, 11760, 15479, 20366, 26780, 35174, 46182, 60602, 79473, 104158, 136445, 178654, 233797, 305834, 399881
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Base Polynomial found using census program: ( also in the Salem list as #23): Clear[h, k, a, b, c, d, e, f, g, h, j, k, l, m, p, x]; h[x_] = a + b*x + c*x^2 + d*x^3 + e*x^4 + f*x^5 + g*x^6 + j*x^7 + x^8; n0 = 8; Union[Flatten[Table[If [Abs[x /. NSolve[h[x] == 0, x][[n0]]] - Max[Abs[Table[ x /. NSolve[h[x] == 0, x][[n]], {n,1, n0}]]] == 0 && Im[x /. NSolve[h[x] == 0, x][[n0]]] ==0 && Sort[Abs[Table[x /.NSolve[h[x] == 0, x][[n]], {n, 1, n0}]]][[n0 - 1]] <= 1 &&Sort[Abs[Table[x /. NSolve[h[x] == 0,x][[n]], {n, 1, n0}]]][[1]] > 0, {Sort[Abs[Table[x /.NSolve[h[x] == 0, x][[n]], {n, 1, n0}]]], h[x]}, {}], {a, -1,1}, {b, -1, 1}, {c, -1, 1}, {d, -1, 1}, {e, -1, 1}, {f, -1,1}, {g, -1, 1}, {j, -1, 1}], 7]]
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REFERENCES
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http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html
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FORMULA
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Coefficient expansion of : 1/(1 - x^3 - x^4 - x^5 + x^8)^2= 1/(-1+ 2 x^3 + 2 x^4 + 2 x^5 - x^6 - 2 x^7 - 5x^8 - 2 x^9 - x^10 + 2 x^11 + 2 x^12 + 2 x^13 - x^16)
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MATHEMATICA
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f[x_] = 1 - x^3 - x^4 - x^5 + x^8; g[x] = ExpandAll[f[x]*x^8*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: A038715 A057040 A096235 this_sequence A143596 A091712 A125721
Adjacent sequences: A147848 A147849 A147850 this_sequence A147852 A147853 A147854
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 15 2008
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