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 A071983 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. 6
 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, 38838893, 68361609, 140571720, 280217025, 204853870, 738704986, 2368147377 (list; graph; refs; listen; history; text; internal format)
 OFFSET 15,9 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, Jun 16 2005 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. LINKS Carlos Rivera, Puzzle 311: Sum to a cube 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. CROSSREFS Cf. A071984. Cf. A090460, A090461. Cf. A078107 (n for which there is no solution). Sequence in context: A327377 A095200 A090460 * A302693 A327881 A215514 Adjacent sequences:  A071980 A071981 A071982 * A071984 A071985 A071986 KEYWORD more,nice,nonn AUTHOR William Rex Marshall, Jun 16 2002 EXTENSIONS a(43)-a(45) from Donovan Johnson, Sep 14 2010 a(46)-a(47) from Jud McCranie, Aug 18 2018 a(48) from Jud McCranie, Sep 17 2018 a(49)-a(52) from Bert Dobbelaere, Dec 30 2018 STATUS approved

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Last modified October 18 20:42 EDT 2019. Contains 328197 sequences. (Running on oeis4.)