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 zeros in the (3,1) and (4,1)-entries), and is zero elsewhere.
This is row 8 of Kløve's Table 3.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000(first 93 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.
Index entries for linear recurrences with constant coefficients, signature (1,3,3,13,21,19,3,-7,-9,-5,-3,-3,-1).
FORMULA
From Nathaniel Johnston, Apr 10 2011: (Start)
(End)
G.f.: x*(x^6 +x^5 -x^4 -x^3 -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 13 2014
MAPLE
MATHEMATICA
LinearRecurrence[{1, 3, 3, 13, 21, 19, 3, -7, -9, -5, -3, -3, -1}, {0, 1, 2, 4, 12, 42, 138, 414, 1235, 3764, 11604, 35664, 109132}, 30] (* Harvey P. Dale, Dec 27 2015 *)
PROG
(PARI) concat(0, Vec(x*(x^6 +x^5 -x^4 -x^3 -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 13 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 01 2011
EXTENSIONS
Name and comments edited, and a(12)-a(28) from Nathaniel Johnston, Apr 10 2011
STATUS
approved