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0, 0, 2, 4, 12, 32, 108, 336, 1036, 3120, 9540, 29244, 89768, 274788, 840936, 2573972, 7881922, 24135000, 73897320, 226249264, 692714696, 2120941424, 6493883944, 19882820480, 60876609464, 186390208744, 570684661408, 1747307671896, 5349860697088
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OFFSET
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0,3
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COMMENTS
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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, and p(2) <= 4.
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, ones on its three subdiagonals (with the exception of zeros in the (3,1), (4,1), and (5,2)-entries), and is zero elsewhere.
This is row 9 of Kløve's Table 3.
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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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G.f.: -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)). - Colin Barker, Dec 16 2014
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MAPLE
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with(LinearAlgebra):
A002528:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[3, 1] and [i, j]<>[4, 1] and [i, j]<>[5, 2], 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} != {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 07 2016, adapted from Maple *)
CoefficientList[Series[2 x^2 / ((1 - x) (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)), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 07 2016
LinearRecurrence[{2, 2, 0, 10, 8, -2, -16, -10, -2, 4, 2, 0, 2, 1}, {0, 0, 2, 4, 12, 32, 108, 336, 1036, 3120, 9540, 29244, 89768, 274788}, 20] (* Harvey P. Dale, Jan 04 2020 *)
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PROG
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(PARI) concat([0, 0], Vec(-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)) + O(x^100))) \\ Colin Barker, Dec 16 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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