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 (with the exception of a single zero in the (1,4)-entry), ones on its three subdiagonals (with the exception of a single zero in the (4,1)-entry), and is zero elsewhere.
This is row 5 of Kløve's Table 3.
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..100
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.
FORMULA
G.f.: -x*(x^3+x^2-1)*(x^3+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).
MAPLE
a:= n-> (Matrix(13, (i, j)-> `if`(i=j-1, 1, `if`(i=13, [-1, -3, -3, -5, -9, -7, 3, 19, 21, 13, 3, 3, 1][j], 0)))^n. <<0, 0, 1, (0$6), 1, 2, 6, 14>>)[9, 1]: seq(a(n), n=0..30); # Alois P. Heinz, Apr 08 2011
MATHEMATICA
a[n_] := ((Table[Which[i == j-1, 1, i == 13, {-1, -3, -3, -5, -9, -7, 3, 19, 21, 13, 3, 3, 1}[[j]], True, 0], {i, 1, 13}, {j, 1, 13}] // MatrixPower[#, n]&).{0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 6, 14})[[9]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 01 2011
EXTENSIONS
Name and comments edited by Nathaniel Johnston, Apr 08 2011
STATUS
approved