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0, 0, 2, 6, 18, 46, 146, 460, 1436, 4352, 13252, 40532, 124396, 381140, 1166708, 3570684, 10932274, 33475170, 102499334, 313825690, 960844358, 2941873064, 9007393480, 27578681888, 84439657768, 258534813320, 791574775192, 2423623112104, 7420586212184, 22720153701768, 69563959091138
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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 and p(j) <= 2+j for j = 1,2.
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 (4,1) and (5,2)-entries), and is zero elsewhere.
This is row 3 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^4+x^3-x^2-x-1) / (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). - Alois P. Heinz, Apr 08 2011
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MAPLE
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with (LinearAlgebra):
A002529:= n-> `if` (n<=1, 0, Permanent (Matrix (n, (i, j)->
`if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2], 1, 0)))):
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MATHEMATICA
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a[n_] := If [n <= 1, 0, Permanent[Table[If[Abs[j-i]<4 && {i, j} != {4, 1} && {i, j} != {5, 2}, 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 12 2014, after Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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