



0, 0, 2, 4, 7, 20, 72, 240, 722, 2140, 6508, 20077, 61776, 189056, 577856, 1768380, 5416230, 16587984, 50788707, 155489884, 476058864, 1457605616, 4462928950, 13664497400, 41837412392, 128096408137, 392202398144, 1200835918016, 3676688064688
(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(j) <= 1+j for j=1,2, and p(4) >= 2.
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 (with the exception of a zero in the (1,4)entry), ones on its three subdiagonals (with the exception of zeros in the (3,1), (4,1), (4,2), and (5,2)entries), and is zero elsewhere.
This is row 12 of Kløve's Table 3.


LINKS

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


FORMULA

G.f.: x^2*(x^9 +2*x^8 2*x^4 2*x^3 5*x^2 +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

with(LinearAlgebra):
A188497:= n> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)>
`if` (abs(ji)<4 and [i, j]<>[1, 4] and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[4, 2] and [i, j]<>[5, 2], 1, 0)))):


MATHEMATICA

a[n_] := Permanent[Table[If[Abs[j  i] < 4 && {i, j} != {1, 4} && {i, j} != {3, 1} && {i, j} != {4, 1} && {i, j} != {4, 2} && {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}](* JeanFrançois Alcover, Jan 07 2016, adapted from Maple *)
CoefficientList[Series[x^2 (x^9 + 2 x^8  2 x^4  2 x^3  5 x^2 + 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(x^2*(x^9 +2*x^8 2*x^4 2*x^3 5*x^2 +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



EXTENSIONS



STATUS

approved



