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A002529 a(n) = A002527(n+1) - A002527(n) - A002526(n).
(Formerly M1620 N0633)
79
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 (list; graph; refs; listen; history; text; internal format)
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-by-n matrix that has ones on its diagonal, ones on its three superdiagonals, ones on its three subdiagonals (with the exception of zeroes in the (4,1) and (5,2)-entries), and is zero elsewhere.

This is row 3 of Klove's Table 3.

REFERENCES

R. Lagrange, Quelques re'sultats dans la me'trique des permutations, Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure, Paris, 79 (1962), 199-241.

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 Klove, 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 re'sultats dans la me'trique des permutations, Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure, Paris, 79 (1962), 199-241.

FORMULA

a(n) = A188379(n+1) - A188492(n) - A188493(n). - Nathaniel Johnston, Apr 08 2011

G.f.: 2*x^2 * (x^4+x^3-x^2-x-1) / (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 08 2011

MAPLE

with (LinearAlgebra):

A002529:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->

              `if` (abs(j-i)<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[j-i]<4 && {i, j} != {4, 1} && {i, j} != {5, 2}, 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Mar 12 2014, after Maple *)

CROSSREFS

Sequence in context: A232600 A140960 A072827 * A217526 A018027 A218759

Adjacent sequences:  A002526 A002527 A002528 * A002530 A002531 A002532

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified September 24 00:01 EDT 2014. Contains 247192 sequences.