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A080018 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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963.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

LINKS

Alois P. Heinz, Rows n = 0..20, flattened

EXAMPLE

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.

MAPLE

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:

seq(T(n), n=0..10);  # Alois P. Heinz, Jul 03 2013

MATHEMATICA

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 *)

CROSSREFS

Row sums = A000142, first column = A001883, second column = A001884, third column = A001885, fourth column = A001886.

Main diagonal and lower diagonal give: A000045(n+1), A178523. - Alois P. Heinz, Jul 03 2013

Sequence in context: A110657 A071512 A263136 * A079686 A005813 A049262

Adjacent sequences:  A080015 A080016 A080017 * A080019 A080020 A080021

KEYWORD

nonn,tabl

AUTHOR

Vladeta Jovovic, Vladimir Baltic, Jan 20 2003

STATUS

approved

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Last modified July 21 17:54 EDT 2019. Contains 325198 sequences. (Running on oeis4.)