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 A188491 Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i, p(1) <= 3, and p(4) >= 2. 7
 0, 1, 2, 6, 14, 48, 152, 476, 1425, 4340, 13288, 40852, 125124, 382888, 1171612, 3587505, 10985790, 33638142, 102988410, 315318756, 965432832, 2955964296, 9050522241, 27710613432, 84843476928, 259771465608, 795361704776, 2435217884992 (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 a single zero in the (1,4)-entry), ones on its three subdiagonals (with the exception of a single zero in the (4,1)-entry), and is zero elsewhere. This is row 5 of Kløve's Table 3. LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..100 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 a(n) = A002526(n-1) + A002528(n-1) + A188494(n-1). - Nathaniel Johnston, Apr 08 2011 G.f.: -x*(x^3+x^2-1)*(x^3+2*x^2+x+1) / (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). MAPLE a:= n-> (Matrix(13, (i, j)-> `if`(i=j-1, 1, `if`(i=13, [-1, -3, -3, -5, -9, -7, 3, 19, 21, 13, 3, 3, 1][j], 0)))^n. <<0, 0, 1, (0\$6), 1, 2, 6, 14>>)[9, 1]: seq(a(n), n=0..30);  # Alois P. Heinz, Apr 08 2011 MATHEMATICA a[n_] := ((Table[Which[i == j-1, 1, i == 13, {-1, -3, -3, -5, -9, -7, 3, 19, 21, 13, 3, 3, 1}[[j]], True, 0], {i, 1, 13}, {j, 1, 13}] // MatrixPower[#, n]&).{0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 6, 14})[]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *) CROSSREFS Sequence in context: A297708 A284701 A011455 * A295974 A324365 A346208 Adjacent sequences:  A188488 A188489 A188490 * A188492 A188493 A188494 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 01 2011 EXTENSIONS Name and comments edited by Nathaniel Johnston, Apr 08 2011 STATUS approved

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Last modified September 22 13:48 EDT 2021. Contains 347607 sequences. (Running on oeis4.)