



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
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OFFSET

0,3


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.


FORMULA

a(n) = A002527(n1) + A188495(n1) + A188496(n1).  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^83*x^7 19*x^621*x^5 13*x^43*x^3 3*x^2x+1).  Alois P. Heinz, Apr 09 2011


MAPLE

with (LinearAlgebra):
A188492:= n> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)>
`if` (abs(ji)<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[ji] < 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}] (* JeanFrançois Alcover, Jan 06 2016, adapted from Maple *)


CROSSREFS

Sequence in context: A127546 A192484 A217861 * A263732 A263733 A263734
Adjacent sequences: A188489 A188490 A188491 * A188493 A188494 A188495


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 01 2011


EXTENSIONS

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


STATUS

approved



