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A035481 Number of n X n symmetric matrices whose first row is 1..n and whose rows and columns are all permutations of 1..n. 6
1, 1, 1, 1, 4, 6, 456, 6240, 10936320, 1225566720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The odd subsequence is presumably A000438, which gives more terms. The even subsequence is A035483.

LINKS

Table of n, a(n) for n=0..9.

EXAMPLE

a(3) = 1 because after 123 in the first row and column, 213 is not allowed for the second row, so it must be 231 and thus the third row is 312.

MATHEMATICA

(* This script is not suitable for n > 6 *) matrices[n_ /; n > 1] := Module[{a, t, vars}, t = Table[Which[i==1, j, j==1, i, j>i, a[i, j], True, a[j, i]], {i, n}, {j, n}]; vars = Select[Flatten[t], !IntegerQ[#]& ] // Union; t /. {Reduce[And @@ (1 <= # <= n & /@ vars) && And @@ Unequal @@@ t, vars, Integers] // ToRules}]; a[0] = a[1] = 1; a[n_] := Length[ matrices[n]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 6}] (* Jean-Fran├žois Alcover, Jan 04 2016 *)

CROSSREFS

Cf. A000438, A035482, A000315, A002860, A003090, A040082.

Sequence in context: A113838 A056831 A027717 * A061214 A137024 A054264

Adjacent sequences:  A035478 A035479 A035480 * A035482 A035483 A035484

KEYWORD

more,nonn,nice

AUTHOR

Joshua Zucker and Joe Keane

STATUS

approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)