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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 (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

Table of n, a(n) for n=15..45.

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: A028852 A095200 A090460 * A215514 A215347 A186247

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

STATUS

approved

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Last modified July 28 12:39 EDT 2017. Contains 289889 sequences.