

A188498


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


3



0, 1, 2, 3, 8, 30, 102, 308, 905, 2744, 8473, 26112, 79924, 244204, 747160, 2288521, 7009458, 21461803, 65704200, 201162258, 615922714, 1885853660, 5774072225, 17678809840, 54128358209, 165728860112, 507424764216, 1553620027784, 4756831354752
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OFFSET

0,3


COMMENTS

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 zeros in the (1,3) and (1,4)entries), ones on its three subdiagonals (with the exception of zeros in the (3,1) and (4,1)entries), and is zero elsewhere.
This is row 13 of Kløve's Table 3.


LINKS

Table of n, a(n) for n=0..28.
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

From Nathaniel Johnston, Apr 11 2011: (Start)
a(n) = A188497(n+1)  A188494(n).
a(n) = A002526(n1) + A002526(n2).
(End)
G.f.: (x^10+2*x^9+x^8 2*x^62*x^52*x^4 3*x^3+x) / (x^14+2*x^13+2*x^11 +4*x^102*x^910*x^8 16*x^72*x^6+8*x^5 +10*x^4+2*x^2+2*x1).


MAPLE

with(LinearAlgebra):
A188498:= n> `if` (n=0, 0, Permanent (Matrix (n, (i, j)>
`if` (abs(ji)<4 and [i, j]<>[1, 3] and [i, j]<>[1, 4] and [i, j]<>[3, 1] and [i, j]<>[4, 1], 1, 0)))):
seq (A188498(n), n=0..20);


MATHEMATICA

a[n_] := Permanent[Table[If[Abs[j  i] < 4 && {i, j} != {1, 3} && {i, j} != {1, 4} && {i, j} != {3, 1} && {i, j} != {4, 1}, 1, 0], {i, 1, n}, {j, 1, n}]]; a[1] = 1; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* JeanFrançois Alcover, Jan 07 2016, adapted from Maple *)
CoefficientList[Series[(x^10 + 2 x^9 + x^8  2 x^6  2 x^5  2 x^4  3 x^3 + x) / (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


PROG

(PARI) concat(0, Vec((x^10+2*x^9+x^8 2*x^62*x^52*x^4 3*x^3+x) / (x^14+2*x^13+2*x^11 +4*x^102*x^910*x^8 16*x^72*x^6+8*x^5 +10*x^4+2*x^2+2*x1) + O(x^40))) \\ Michel Marcus, Dec 12 2014


CROSSREFS

Sequence in context: A186927 A177010 A004106 * A012886 A078918 A054104
Adjacent sequences: A188495 A188496 A188497 * A188499 A188500 A188501


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 01 2011


EXTENSIONS

Name and comments edited, and a(12)a(28) from Nathaniel Johnston, Apr 11 2011


STATUS

approved



