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Search: id:A084202
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| A084202 |
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G.f. A(x) defined by: A(x)^2 consists entirely of integer coefficients between 1 and 2 (A083952); A(x) is the unique power series solution with A(0)=1. |
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17
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| 1, 1, 0, 1, 0, 1, -1, 2, -2, 4, -6, 10, -16, 27, -44, 75, -127, 218, -375, 650, -1130, 1974, -3460, 6086, -10736, 18993, -33685, 59882, -106683, 190446, -340611, 610243, -1095102, 1968200, -3542468, 6384518, -11521308, 20815942, -37651528, 68176596, -123574852, 224204708, -407153894
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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Limit a(n)/a(n+1) -> r = -0.530852489019085 where A(r)=0.
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LINKS
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N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
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MATHEMATICA
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a[n_] := a[n] = Block[{s = Sum[a[i]*x^i, {i, 0, n - 1}]}, If[ IntegerQ@ Last@ CoefficientList[ Series[ Sqrt[s + x^n], {x, 0, n}], x], 1, 2]]; Table[a[n], {n, 0, 42}]; CoefficientList[ Series[ Sqrt[ Sum[ a[i]*x^i, {i, 0, 42}]], {x, 0, 42}], x] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 11 2007 *)
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CROSSREFS
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Cf. A083952, A084203-A084212.
Sequence in context: A006355 A055389 A163733 this_sequence A053637 A000016 A060553
Adjacent sequences: A084199 A084200 A084201 this_sequence A084203 A084204 A084205
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 19 2003
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