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A080061
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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 0<=i-j<=2 else m(i,j)=1.
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7
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1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 1, 4, 8, 10, 1, 5, 21, 38, 34, 21, 1, 33, 122, 209, 206, 109, 40, 1, 236, 849, 1400, 1351, 836, 295, 72, 1, 1918, 6719, 10849, 10543, 6629, 2821, 715, 125, 1, 17440, 59873, 95516, 92708, 60284, 26870, 8372, 1604, 212, 1, 175649, 593686
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OFFSET
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0,9
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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J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963.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 (See A001883)
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LINKS
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EXAMPLE
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1;
0,1;
0,1,1;
0,1,4,1;
1,4,8,10,1;
5,21,38,34,21,1;
... P(5; x) = Permanent(Matrix(5, 5, [[x,1,1,1,1],[x,x,1,1,1],[x,x,x,1,1],[1,x,x,x,1],[1,1,x,x,x]]))= 5+21*x+38*x^2+34*x^3+21*x^4+x^5.
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MAPLE
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local M, r, c, p, pord ;
if n = 0 then
return [1] ;
else
M := Matrix(n, n) ;
for r to n do
for c to n do
if r-c >=0 and r-c <=2 then
M[r, c] := x ;
else
M[r, c] := 1 ;
end if;
end do:
end do:
p := LinearAlgebra[Permanent](M) ;
pord := degree(p) ;
[seq( coeff(p, x, r), r=0..pord)] ;
end if;
end proc:
for n from 0 to 10 do
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MATHEMATICA
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M[n_] := Table[If[0 <= i-j <= 2, x, 1], {i, 1, n}, {j, 1, n}]; M[0]={{1}}; Table[CoefficientList[Permanent[M[n]], x], {n, 0, 10}] // Flatten (* Jean-François Alcover, Jan 06 2016 *)
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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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