



0, 0, 2, 4, 10, 28, 96, 304, 928, 2784, 8504, 26124, 80228, 245544, 751168, 2299184, 7040986, 21561028, 66015398, 202114264, 618817376, 1894692160, 5801169248, 17761879056, 54382725520, 166507388264, 509808051944, 1560917463152, 4779176035680
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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(1) <= 2, p(2) <= 4, 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 (3,1), (4,1), and (5,2)entries), and is zero elsewhere.
This is row 11 of Kløve's Table 3.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
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.
Index entries for linear recurrences with constant coefficients, signature (1,3,3,13,21,19,3,7,9,5,3,3,1).


FORMULA

a(n) = A002527(n1) + A188495(n1).  Nathaniel Johnston, Apr 11 2011
G.f.: x^2*(2*x +2)/(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).  Colin Barker, Dec 13 2014


MAPLE

with(LinearAlgebra):
A188496:= n> `if`(n<=1, 0, Permanent(Matrix(n, (i, j)>
`if`(abs(ji)<4 and [i, j]<>[1, 4] and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):
seq(A188496(n), n=0..20);


MATHEMATICA

a[n_] := Permanent[Table[If[Abs[j  i] < 4 && {i, j} != {1, 4} && {i, j} != {3, 1} && {i, j} != {4, 1} && {i, j} != {5, 2}, 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 *)
LinearRecurrence[{1, 3, 3, 13, 21, 19, 3, 7, 9, 5, 3, 3, 1}, {0, 0, 2, 4, 10, 28, 96, 304, 928, 2784, 8504, 26124, 80228}, 30] (* Harvey P. Dale, Aug 31 2016 *)


PROG

(PARI) concat([0, 0], Vec(x^2*(2*x +2)/(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) + O(x^100))) \\ Colin Barker, Dec 13 2014


CROSSREFS

Sequence in context: A271207 A091175 A090594 * A191501 A085549 A022492
Adjacent sequences: A188493 A188494 A188495 * A188497 A188498 A188499


KEYWORD

nonn,easy


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



