This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A188379 #33 Jan 07 2016 02:55:06
%S A188379 0,0,0,6,18,46,115,374,1204,3752,11300,34324,105124,322989,989692,
%T A188379 3028484,9267328,28374898,86891022,266058106,814585879,2494006074,
%U A188379 7636057864,23380074400,71584762200,219176102664,671066472872,2054652945289
%N A188379 a(n) = A002526(n+1) - A002527(n+1).
%C A188379 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.
%C A188379 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.
%C A188379 This is row 4 of Kløve's Table 3.
%H A188379 Torleiv Kløve, <a href="http://www.ii.uib.no/publikasjoner/texrap/pdf/2008-376.pdf"> Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. </a> Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.
%F A188379 a(n) = A002529(n-1) + A188492(n-1) + A188493(n-1). - _Nathaniel Johnston_, Apr 08 2011
%F A188379 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*x-1). - _Alois P. Heinz_, Apr 07 2011
%p A188379 with (LinearAlgebra):
%p A188379 A188379:= n-> `if` (n<=2, 0, Permanent (Matrix (n, (i, j)->
%p A188379 `if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2] and [i, j]<>[6, 3], 1, 0)))):
%p A188379 seq (A188379(n), n=0..20);
%t A188379 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}] (* _Jean-François Alcover_, Jan 07 2016, adapted from Maple *)
%t A188379 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 *)
%K A188379 nonn
%O A188379 0,4
%A A188379 _N. J. A. Sloane_, Apr 01 2011
%E A188379 Name and comments edited by _Nathaniel Johnston_, Apr 08 2011