A188492 a(n) = A002526(n+2) + A002526(n) - A002527(n+2) - A002527(n+1) + A002527(n) - A188493(n).

0, 0, 2, 6, 14, 38, 124, 400, 1232, 3712, 11288, 34628, 106352, 325772, 996712, 3050352, 9340170, 28602014, 87576426, 268129662, 820931640, 2513509536, 7695861408, 23563048304, 72144604576, 220890113784, 676315440208, 2070725515096

Offset: 0

Author

N. J. A. Sloane, Apr 01 2011

Keywords

• nonn

Comments

For n >= 2, a(n) is the number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i, p(j) <= 2+j for j = 1,2, and p(4) >= 2.

For n >= 2, a(n) is also the permanent of the n X n matrix that has ones on its diagonal, ones on its three superdiagonals (with the exception of a zero in the (1,4)-entry), ones on its three subdiagonals (with the exception of zeros in the (4,1) and (5,2)-entries), and is zero elsewhere.

This is row 6 of Kløve's Table 3.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..89
• Torleiv Kløve, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.

Programs

Maple

with (LinearAlgebra):
A188492:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->
              `if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2] and [i, j]<>[1, 4], 1, 0)))):
seq (A188492(n), n=0..20);

Mathematica

a[n_] := Permanent[Table[If[Abs[j-i] < 4 && {i, j} != {4, 1} && {i, j} != {5, 2} && {i, j} != {1, 4}, 1, 0], {i, 1, n}, {j, 1, n}] ]; a[1] = 0; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

Formula

a(n) = A002527(n-1) + A188495(n-1) + A188496(n-1). - Nathaniel Johnston, Apr 08 2011

G.f.: 2*x^2 * (x^2+2*x+1) / (x^13+3*x^12+3*x^11 +5*x^10+9*x^9 +7*x^8-3*x^7 -19*x^6-21*x^5 -13*x^4-3*x^3 -3*x^2-x+1). - Alois P. Heinz, Apr 09 2011

Extensions

Name and comments edited, and a(12)-a(27) from Nathaniel Johnston, Apr 08 2011