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Search: id:A083691
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| A083691 |
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Length of list generated by n replacements of k by {-1-|k|, .., 1+|k|} with increment 2, starting with {0}. |
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+0
3
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| 1, 2, 6, 20, 76, 296, 1240, 5200, 22960, 100512, 458592, 2064704, 9633472, 44237440, 209780096, 977536256, 4693031680, 22117091840, 107211650560, 509817656320, 2490609167360, 11930278307840, 58656838113280, 282679983493120
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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G.f. from SuperSeeker (LISTTOALGEQ) checked up to n=11. Same sequence starting with {1}: see A083692. Sum of absolute values of list elements gives A083693. Cross-references cite sequences with similar generation by integer-substitution and length of resulting lists.
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FORMULA
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CoefficientList[InverseSeries[Series[(-4n-5n^2+n^2Sqrt[1+8n+8n^2])/ (2(-2-6n-6n^2-2n^3)), {n, 0, 12}]], n], apart from initial zero.
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EXAMPLE
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0, 1 and 2 substitutions produce lengths 1, 2 and 6:
{0}; {-1,1}; {-2,0,2, -2,0,2};
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MATHEMATICA
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Table[Length@Flatten[Nest[ #/.k_Integer:>Table[i, {i, -1-Abs[k], Abs[k]+1, 2}]&, {0}, w]], {w, 0, 10}]
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CROSSREFS
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Cf. A000108, A001003, A006319.
Sequence in context: A134957 A052889 A150169 this_sequence A150170 A150171 A150172
Adjacent sequences: A083688 A083689 A083690 this_sequence A083692 A083693 A083694
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 03 2003
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