|
%I #26 Jan 06 2016 13:53:25
%S 0,0,2,6,14,38,124,400,1232,3712,11288,34628,106352,325772,996712,
%T 3050352,9340170,28602014,87576426,268129662,820931640,2513509536,
%U 7695861408,23563048304,72144604576,220890113784,676315440208,2070725515096
%N a(n) = A002526(n+2) + A002526(n) - A002527(n+2) - A002527(n+1) + A002527(n) - A188493(n).
%C 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.
%C 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.
%C This is row 6 of Kløve's Table 3.
%H Nathaniel Johnston, <a href="/A188492/b188492.txt">Table of n, a(n) for n = 0..89</a>
%H Torleiv Kløve, <a href="http://www.ii.uib.no/publikasjoner/texrap/pdf/2008-376.pdf"> Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. </a> Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.
%F a(n) = A002527(n-1) + A188495(n-1) + A188496(n-1). - _Nathaniel Johnston_, Apr 08 2011
%F 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
%p with (LinearAlgebra):
%p A188492:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->
%p `if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2] and [i, j]<>[1, 4], 1, 0)))):
%p seq (A188492(n), n=0..20);
%t 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 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 01 2011
%E Name and comments edited, and a(12)-a(27) from _Nathaniel Johnston_, Apr 08 2011
|
