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A332566
a(n) is the permanent of an n X n symmetric Toeplitz matrix M(n) whose first row consists of a single zero followed by successive positive integers repeated (A004526).
4
1, 0, 1, 2, 16, 150, 2333, 45840, 1227816, 40715300, 1701223409, 84902728550, 5108474886424, 357837483830570, 29336856811970045, 2745407159100236484, 294324995624694053072, 35473014438701226021416, 4818705384665419284918401, 727012502373285844943278058, 122057159014198483893887865744
OFFSET
0,4
LINKS
Wikipedia, Symmetric matrix
Wikipedia, Toeplitz Matrix
EXAMPLE
For n = 4 the matrix M(4) is
0 1 1 2
1 0 1 1
1 1 0 1
2 1 1 0
with permanent a(4) = 16.
MATHEMATICA
nmax:=20; k[i_]:=Floor[i/2]; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Array[k, n], Array[k, n]]]]; Table[a[n], {n, 0, nmax}]
PROG
(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, floor(j/2), if (j==1, floor(i/2))))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
a(n) = matpermanent(tm(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Feb 16 2020
STATUS
approved