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A002528 a(n) = A188491(n+1) - A188494(n) - A002526(n).
(Formerly M1256 N0480)
5
0, 0, 2, 4, 12, 32, 108, 336, 1036, 3120, 9540, 29244, 89768, 274788, 840936, 2573972, 7881922, 24135000, 73897320, 226249264, 692714696, 2120941424, 6493883944, 19882820480, 60876609464, 186390208744, 570684661408, 1747307671896, 5349860697088 (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, p(1) <= 2, and p(2) <= 4.

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 (3,1), (4,1), and (5,2)-entries), and is zero elsewhere.

This is row 9 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

Nathaniel Johnston, Table of n, a(n) for n = 0..90

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), 199-241.

Index entries for linear recurrences with constant coefficients, signature (2,2,0,10,8,-2,-16,-10,-2,4,2,0,2,1).

FORMULA

a(n) = A002527(n-1) + A188491(n-1). - Nathaniel Johnston, Apr 10 2011

G.f.: -2*x^2 / ((x -1)*(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 16 2014

MAPLE

with(LinearAlgebra):

A002528:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->

              `if` (abs(j-i)<4 and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):

MATHEMATICA

a[n_] := Permanent[Table[If[Abs[j - i] < 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}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)

CoefficientList[Series[2 x^2 / ((1 - x) (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)), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 07 2016

PROG

(PARI) concat([0, 0], Vec(-2*x^2 / ((x -1)*(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 16 2014

CROSSREFS

Sequence in context: A161177 A039721 A148193 * A216818 A216819 A216820

Adjacent sequences:  A002525 A002526 A002527 * A002529 A002530 A002531

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Name and comments edited, and a(12)-a(28) from Nathaniel Johnston, Apr 10 2011

STATUS

approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)