



0, 0, 2, 6, 18, 46, 146, 460, 1436, 4352, 13252, 40532, 124396, 381140, 1166708, 3570684, 10932274, 33475170, 102499334, 313825690, 960844358, 2941873064, 9007393480, 27578681888, 84439657768, 258534813320, 791574775192, 2423623112104, 7420586212184, 22720153701768, 69563959091138
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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 and p(j) <= 2+j for j = 1,2.
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, 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 3 of Kløve's Table 3.


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Alois P. Heinz, 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.
R. Lagrange, Quelques résultats dans la métrique des permutations, Annales Scientifiques de l'École Normale Supérieure, Paris, 79 (1962), 199241.


FORMULA

a(n) = A188379(n+1)  A188492(n)  A188493(n).  Nathaniel Johnston, Apr 08 2011
G.f.: 2*x^2 * (x^4+x^3x^2x1) / (x^14+2*x^13+2*x^11 +4*x^10 2*x^9 10*x^8 16*x^72*x^6 +8*x^5+10*x^4 +2*x^2+2*x1).  Alois P. Heinz, Apr 08 2011


MAPLE

with (LinearAlgebra):
A002529:= n> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)>
`if` (abs(ji)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):
seq (A002529(n), n=0..20);


MATHEMATICA

Permanent[m_] := With[{v = Array[x, Length[m]]}, Coefficient[Times @@ (m.v), Times @@ v]]; a[n_] := If [n <= 1, 0, Permanent[Table[If[Abs[ji]<4 && {i, j} != {4, 1} && {i, j} != {5, 2}, 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[a[n], {n, 0, 30}] (* JeanFrançois Alcover, Mar 12 2014, after Maple *)


CROSSREFS

Sequence in context: A140960 A072827 A248169 * A217526 A018027 A218759
Adjacent sequences: A002526 A002527 A002528 * A002530 A002531 A002532


KEYWORD

nonn,changed


AUTHOR

N. J. A. Sloane


EXTENSIONS

Name and comments edited and terms a(12)a(30) from Nathaniel Johnston, Apr 08 2011


STATUS

approved



