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A071983
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Square chains: the number of permutations (reversals not counted as different) of the numbers 1 to n such that the sum of any two consecutive numbers is a square.
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6
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1, 1, 1, 0, 0, 0, 0, 0, 3, 0, 10, 12, 35, 52, 19, 20, 349, 392, 669, 4041, 17175, 12960, 14026, 11889, 29123, 39550, 219968, 553694, 2178103, 5301127, 12220138
(list; graph; refs; listen; history; internal format)
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OFFSET
| 15,9
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COMMENTS
| For n > 31, this sequence counts each circular solution (in which the first and last numbers also sum to a square) n times. Sequence A090460 counts the circular solutions only once, giving the number of essentially different solutions.
The existence of cubic chains in answered affirmatively in Puzzle 311. - T. D. Noe (noe(AT)sspectra.com), Jun 16 2005
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REFERENCES
| Ruemmler, Ronald E., "Square Loops," Journal of Recreational Mathematics 14:2 (1981-82), page 141; Solution by Chris Crandell and Lance Gay, JRM 15:2 (1982-83), page 155.
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LINKS
| Carlos Rivera, Puzzle 311: Sum to a cube
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EXAMPLE
| There is only one possible square chain of minimum length, which is: (8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9) so a(15)=1.
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CROSSREFS
| Cf. A071984.
Cf. A090460, A090461.
Cf. A078107 (n for which there is no solution).
Sequence in context: A028852 A095200 A090460 * A094897 A019264 A028851
Adjacent sequences: A071980 A071981 A071982 * A071984 A071985 A071986
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KEYWORD
| more,nice,nonn
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AUTHOR
| William Rex Marshall (w.r.marshall(AT)actrix.co.nz), Jun 16 2002
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EXTENSIONS
| a(43)-a(45) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 14 2010
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