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A095986 A card-arranging problem: number of permutations p_1, ..., p_n of 1, ..., n such that i + p_i is a square for every i. 5
1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 4, 3, 2, 5, 15, 21, 66, 37, 51, 144, 263, 601, 1333, 2119, 2154, 2189, 3280, 12405, 55329, 160895, 588081, 849906, 1258119, 1233262, 2478647, 4305500, 17278636, 47424179, 153686631, 396952852, 1043844982 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,15
COMMENTS
Gardner attributes the problem (for the case n = 13) to David L. Silverman.
REFERENCES
M. Gardner, Mathematical Games column, Scientific American, Nov 1974.
M. Gardner, Mathematical Games column, Scientific American, Mar 1975.
M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 81.
LINKS
FORMULA
a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether i+j is a square or not.
EXAMPLE
a(0) = 1: the empty permutation.
a(3) = 1: 321.
a(5) = 1: 32154.
a(8) = 1: 87654321.
a(9) = 1: 826543917.
MAPLE
b:= proc(s) option remember; (n-> `if`(n=0, 1, add(
`if`(issqr(n+j), b(s minus {j}), 0), j=s)))(nops(s))
end:
a:= n-> b({$1..n}):
seq(a(n), n=0..25); # Alois P. Heinz, Mar 03 2024
MATHEMATICA
nmax=45; a[n_]:=Permanent[Table[If[IntegerQ[Sqrt[i+j]], 1, 0], {i, n}, {j, n}]]; Join[{1}, Array[a, nmax]] (* Stefano Spezia, Mar 03 2024 *)
CROSSREFS
Cf. A006063 (for cubes), A010052, A073364.
Sequence in context: A329876 A128868 A341073 * A212637 A283273 A269599
KEYWORD
nonn,hard,more,changed
AUTHOR
EXTENSIONS
a(32) and a(33) from John W. Layman, Jul 21 2004
a(34)-a(36) from Ray Chandler, Jul 26 2004
a(37)-a(45) from William Rex Marshall, Apr 18 2006
a(0)=1 prepended by Alois P. Heinz, Mar 03 2024
STATUS
approved

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Last modified March 19 07:21 EDT 2024. Contains 370955 sequences. (Running on oeis4.)