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A188495
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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(4) >= 2.
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6
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0, 1, 2, 4, 10, 36, 120, 368, 1089, 3304, 10168, 31312, 95880, 293120, 896824, 2746569, 8411818, 25756220, 78853410, 241421436, 739183568, 2263249600, 6929580817, 21216729488, 64960656448, 198894856144, 608971496032, 1864533223584, 5708777321872
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OFFSET
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0,3
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COMMENTS
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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) and (4,1)-entries), and is zero elsewhere.
This is row 10 of Kløve's Table 3.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,2,0,10,8,-2,-16,-10,-2,4,2,0,2,1).
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FORMULA
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(End)
G.f.: -x*(x +1)*(x^6 +x^5 -x^4 -x^3 -x^2 -x +1) / ((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)). - Colin Barker, Dec 13 2014
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MAPLE
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with (LinearAlgebra):
A188495:= n-> `if` (n=0, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[1, 4], 1, 0)))):
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MATHEMATICA
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a[n_] := Permanent[Table[If[Abs[j - i] < 4 && {i, j} != {3, 1} && {i, j} != {4, 1} && {i, j} != {1, 4}, 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 06 2016, adapted from Maple *)
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PROG
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(PARI) concat(0, Vec(-x*(x +1)*(x^6 +x^5 -x^4 -x^3 -x^2 -x +1) / ((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)) + O(x^100))) \\ Colin Barker, Dec 13 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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