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, ones on its three subdiagonals (with the exception of a single zero in the (4,1)-entry), and is zero elsewhere.
This is the second row 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 (first 92 terms from Nathaniel Johnston)
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
From Nathaniel Johnston, Apr 03 2011: (Start)
G.f.: x*(x^7+2*x^6-2*x^4-2*x^3-1) / (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 07 2011
MAPLE
MATHEMATICA
A002527[n_] := If [n == 0, 0, Permanent[Table[If [Abs[j-i]<4 && {i, j} != {4, 1}, 1, 0], {i, 1, n}, {j, 1, n}]]]; Table [A002527[n], {n, 0, 25}] (* Jean-François Alcover, Mar 11 2014, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name and comments edited, and terms after a(11) added by Nathaniel Johnston, Apr 03 2011
STATUS
approved