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A306457
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The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive prime numbers prime(1), ..., prime(n) and whose first column consists of prime(1), prime(n + 1), ..., prime(2*n - 1).
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5
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1, 2, 19, 546, 40851, 4747510, 986799301, 292666754602, 135134321711681, 80312872924339660, 55242523096584443271, 52058868505260739019880, 55579419798019716586180451, 72402676504369062268839297084, 120521257466525185305708420453019, 234000358527930078723939842673115488
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OFFSET
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0,2
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COMMENTS
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The trace of the matrix M(n) is A005843(n).
The sum of the first row of the matrix M(n) is A007504(n).
The determinant of the matrix M(n) is A318173(n).
For n > 1, the subdiagonal sum of the matrix M(n) is A306192(n).
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LINKS
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EXAMPLE
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For n = 1 the matrix M(1) is
2
with permanent a(1) = 2.
For n = 2 the matrix M(2) is
2, 3
5, 2
with permanent a(2) = 19.
For n = 3 the matrix M(3) is
2, 3, 5
7, 2, 3
11, 7, 2
with permanent a(3) = 546.
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MAPLE
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f:= proc(n) uses LinearAlgebra; `if`(n=0, 1, Permanent(ToeplitzMatrix([seq(ithprime(i), i=2*n-1..n+1, -1), seq(ithprime(i), i=1..n)]))) end proc: map(f, [$0..15]);
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MATHEMATICA
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p[i_]:=Prime[i]; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{p[1]}, Array[p, n-1, {n+1, 2*n-1}]], Array[p, n]]]]; Array[a, 15, 0]
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PROG
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(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, prime(j), if (j==1, prime(n+i-1))))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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