



0, 0, 0, 6, 18, 46, 115, 374, 1204, 3752, 11300, 34324, 105124, 322989, 989692, 3028484, 9267328, 28374898, 86891022, 266058106, 814585879, 2494006074, 7636057864, 23380074400, 71584762200, 219176102664, 671066472872, 2054652945289
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OFFSET

0,4


COMMENTS

For n >= 3, a(n) is the number of permutations p on the set [n] with the properties that abs(p(i)i) <= 3 for all i and p(j) <= 2+j for j = 1,2,3.
For n >= 3, 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 (4,1),(5,2), and (6,3)entries), and is zero elsewhere.
This is row 4 of Kløve's Table 3.


LINKS



FORMULA

G.f.: (x^10 +2*x^9 +2*x^7 +4*x^6 2*x^5 8*x^4 13*x^3 2*x^2 +6*x+6) * x^3 / (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*x1).  Alois P. Heinz, Apr 07 2011


MAPLE

with (LinearAlgebra):
A188379:= n> `if` (n<=2, 0, Permanent (Matrix (n, (i, j)>
`if` (abs(ji)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2] and [i, j]<>[6, 3], 1, 0)))):


MATHEMATICA

a[n_] := Permanent[Table[If[Abs[j  i] < 4 && {i, j} != {4, 1} && {i, j} != {5, 2} && {i, j} != {6, 3}, 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^10 + 2 x^9 + 2 x^7 + 4 x^6  2 x^5  8 x^4  13 x^3  2 x^2 + 6 x+6) x^3 / (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), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 07 2016 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



