login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188498 Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i, p(1) <= 2, and p(j) >= 2 for j=3,4. 3

%I

%S 0,1,2,3,8,30,102,308,905,2744,8473,26112,79924,244204,747160,2288521,

%T 7009458,21461803,65704200,201162258,615922714,1885853660,5774072225,

%U 17678809840,54128358209,165728860112,507424764216,1553620027784,4756831354752

%N Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i, p(1) <= 2, and p(j) >= 2 for j=3,4.

%C 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 zeros in the (1,3) and (1,4)-entries), ones on its three subdiagonals (with the exception of zeros in the (3,1) and (4,1)-entries), and is zero elsewhere.

%C This is row 13 of Kløve's Table 3.

%H 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 From _Nathaniel Johnston_, Apr 11 2011: (Start)

%F a(n) = A188497(n+1) - A188494(n).

%F a(n) = A002526(n-1) + A002526(n-2).

%F (End)

%F G.f.: -(x^10 + 2*x^9 + x^8 - 2*x^6 - 2*x^5 - 2*x^4 - 3*x^3 + x) / (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).

%p with(LinearAlgebra):

%p A188498:= n-> `if` (n=0, 0, Permanent (Matrix (n, (i, j)->

%p `if` (abs(j-i)<4 and [i, j]<>[1, 3] and [i, j]<>[1, 4] and [i, j]<>[3, 1] and [i, j]<>[4, 1], 1, 0)))):

%p seq (A188498(n), n=0..20);

%t a[n_] := Permanent[Table[If[Abs[j - i] < 4 && {i, j} != {1, 3} && {i, j} != {1, 4} && {i, j} != {3, 1} && {i, j} != {4, 1}, 1, 0], {i, 1, n}, {j, 1, n}]]; a[1] = 1; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* _Jean-François Alcover_, Jan 07 2016, adapted from Maple *)

%t CoefficientList[Series[-(x^10 + 2 x^9 + x^8 - 2 x^6 - 2 x^5 - 2 x^4 - 3 x^3 + x) / (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 *)

%o (PARI) concat(0, Vec(-(x^10+2*x^9+x^8 -2*x^6-2*x^5-2*x^4 -3*x^3+x) / (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) + O(x^40))) \\ _Michel Marcus_, Dec 12 2014

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 01 2011

%E Name and comments edited, and a(12)-a(28) from _Nathaniel Johnston_, Apr 11 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 08:08 EST 2019. Contains 329968 sequences. (Running on oeis4.)