cp's OEIS Frontend

A188496 a(n) = A188492(n+1) - A188495(n) - A002527(n).

%I A188496 #27 Aug 31 2016 12:44:27
%S A188496 0,0,2,4,10,28,96,304,928,2784,8504,26124,80228,245544,751168,2299184,
%T A188496 7040986,21561028,66015398,202114264,618817376,1894692160,5801169248,
%U A188496 17761879056,54382725520,166507388264,509808051944,1560917463152,4779176035680
%N A188496 a(n) = A188492(n+1) - A188495(n) - A002527(n).
%C A188496 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(1) <= 2, p(2) <= 4, and p(4) >= 2.
%C A188496 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), and (5,2)-entries), and is zero elsewhere.
%C A188496 This is row 11 of Kløve's Table 3.
%H A188496 Colin Barker, <a href="/A188496/b188496.txt">Table of n, a(n) for n = 0..1000</a>
%H A188496 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.
%H A188496 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,3,13,21,19,3,-7,-9,-5,-3,-3,-1).
%F A188496 a(n) = A002527(n-1) + A188495(n-1). - _Nathaniel Johnston_, Apr 11 2011
%F A188496 G.f.: x^2*(2*x +2)/(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
%p A188496 with(LinearAlgebra):
%p A188496 A188496:= n-> `if`(n<=1, 0, Permanent(Matrix(n, (i, j)->
%p A188496               `if`(abs(j-i)<4 and [i, j]<>[1, 4] and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):
%p A188496 seq(A188496(n), n=0..20);
%t A188496 a[n_] := Permanent[Table[If[Abs[j - i] < 4 && {i, j} != {1, 4} && {i, j} != {3, 1} && {i, j} != {4, 1} && {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}] (* _Jean-François Alcover_, Jan 06 2016, adapted from Maple *)
%t A188496 LinearRecurrence[{1,3,3,13,21,19,3,-7,-9,-5,-3,-3,-1},{0,0,2,4,10,28,96,304,928,2784,8504,26124,80228},30] (* _Harvey P. Dale_, Aug 31 2016 *)
%o A188496 (PARI) concat([0,0], Vec(x^2*(2*x +2)/(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
%K A188496 nonn,easy
%O A188496 0,3
%A A188496 _N. J. A. Sloane_, Apr 01 2011
%E A188496 Name and comments edited, and a(12)-a(28) from _Nathaniel Johnston_, Apr 11 2011