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A080018
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Triangle of coefficients of polynomials P(n; x) = Permanent(M), where M=[m(i,j)] is n X n matrix defined by m(i,j)=x if -1<=i-j<=1 else m(i,j)=1.
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7
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1, 0, 1, 0, 0, 2, 0, 1, 2, 3, 1, 2, 10, 6, 5, 4, 20, 28, 44, 16, 8, 29, 104, 207, 180, 151, 36, 13, 206, 775, 1288, 1407, 830, 437, 76, 21, 1708, 6140, 10366, 10384, 7298, 3100, 1138, 152, 34, 15702, 55427, 91296, 92896, 63140, 31278, 10048, 2744, 294, 55
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OFFSET
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0,6
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REFERENCES
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J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963. See Table 1. - N. J. A. Sloane, Aug 27 2013
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LINKS
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EXAMPLE
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1;
0, 1;
0, 0, 2;
0, 1, 2, 3;
1, 2, 10, 6, 5;
4, 20, 28, 44, 16, 8;
...
P(4; x) = Permanent(MATRIX([[x, x, 1, 1], [x, x, x, 1], [1, x, x, x], [1, 1, x, x]])) = 1+2*x+10*x^2+6*x^3+5*x^4.
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MAPLE
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with(LinearAlgebra):
T:= proc(n) option remember; local p;
if n=0 then 1 else
p:= Permanent(Matrix(n, (i, j)-> `if`(abs(i-j)<2, x, 1)));
seq(coeff(p, x, i), i=0..n)
fi
end:
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MATHEMATICA
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t[0] = {1}; t[n_] := CoefficientList[Permanent[Array[If[Abs[#1 - #2] < 2, x, 1]&, {n, n}]], x]; Table[t[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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