A188379 a(n) = A002526(n+1) - A002527(n+1).

0, 0, 0, 6, 18, 46, 115, 374, 1204, 3752, 11300, 34324, 105124, 322989, 989692, 3028484, 9267328, 28374898, 86891022, 266058106, 814585879, 2494006074, 7636057864, 23380074400, 71584762200, 219176102664, 671066472872, 2054652945289

Offset

0,4

Comments

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

For n >= 3, a(n) is also the permanent of the n X n matrix that has ones on its diagonal, ones on its three superdiagonals, ones on its three subdiagonals (with the exception of zeros in the (4,1),(5,2), and (6,3)-entries), and is zero elsewhere.

This is row 4 of Kløve's Table 3.

Links

Table of n, a(n) for n=0..27.

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) = A002529(n-1) + A188492(n-1) + A188493(n-1). - Nathaniel Johnston, Apr 08 2011

G.f.: -(x^10 +2*x^9 +2*x^7 +4*x^6 -2*x^5 -8*x^4 -13*x^3 -2*x^2 +6*x+6) * x^3 / (x^14 +2*x^13 +2*x^11 +4*x^10 -2*x^9 -10*x^8 -16*x^7 -2*x^6 +8*x^5 +10*x^4 +2*x^2 +2*x-1). - Alois P. Heinz, Apr 07 2011

Maple

with (LinearAlgebra):
A188379:= n-> `if` (n<=2, 0, Permanent (Matrix (n, (i, j)->
              `if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2] and [i, j]<>[6, 3], 1, 0)))):
seq (A188379(n), n=0..20);

Mathematica

a[n_] := Permanent[Table[If[Abs[j - i] < 4 && {i, j} != {4, 1} && {i, j} != {5, 2} && {i, j} != {6, 3}, 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 07 2016, adapted from Maple *)
CoefficientList[Series[-(x^10 + 2 x^9 + 2 x^7 + 4 x^6 - 2 x^5 - 8 x^4 - 13 x^3 - 2 x^2 + 6 x+6) x^3 / (x^14 + 2 x^13 + 2 x^11 + 4 x^10 - 2 x^9 - 10 x^8 - 16 x^7 - 2 x^6 + 8 x^5 + 10 x^4 + 2 x^2 + 2 x - 1), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 07 2016 *)

Crossrefs

Sequence in context: A304161 A261016 A328890 * A299268 A248462 A256010

Adjacent sequences: A188376 A188377 A188378 * A188380 A188381 A188382

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2011

Extensions

Name and comments edited by Nathaniel Johnston, Apr 08 2011

Status

approved