This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 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
 0, 1, 2, 3, 8, 30, 102, 308, 905, 2744, 8473, 26112, 79924, 244204, 747160, 2288521, 7009458, 21461803, 65704200, 201162258, 615922714, 1885853660, 5774072225, 17678809840, 54128358209, 165728860112, 507424764216, 1553620027784, 4756831354752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. This is row 13 of Kløve's Table 3. LINKS Torleiv Kløve, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008. FORMULA From Nathaniel Johnston, Apr 11 2011: (Start) a(n) = A188497(n+1) - A188494(n). a(n) = A002526(n-1) + A002526(n-2). (End) 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). MAPLE with(LinearAlgebra): A188498:= n-> `if` (n=0, 0, Permanent (Matrix (n, (i, j)->               `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)))): seq (A188498(n), n=0..20); MATHEMATICA 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 *) 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 PROG (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 CROSSREFS Sequence in context: A186927 A177010 A004106 * A012886 A078918 A054104 Adjacent sequences:  A188495 A188496 A188497 * A188499 A188500 A188501 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 01 2011 EXTENSIONS Name and comments edited, and a(12)-a(28) from Nathaniel Johnston, Apr 11 2011 STATUS approved

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