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A188494
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Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(1) <= 2.
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7
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0, 1, 2, 4, 12, 42, 138, 414, 1235, 3764, 11604, 35664, 109132, 333652, 1021220, 3127709, 9578526, 29326904, 89785684, 274896606, 841682902, 2577075290, 7890425175, 24158602552, 73968049928, 226473538032, 693411153800, 2123068036904, 6500352097064
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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, 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 8 of Kløve's Table 3.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,3,3,13,21,19,3,-7,-9,-5,-3,-3,-1).
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FORMULA
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(End)
G.f.: x*(x^6 +x^5 -x^4 -x^3 -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 13 2014
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MAPLE
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with(LinearAlgebra):
A188494:= 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], 1, 0)))):
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MATHEMATICA
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LinearRecurrence[{1, 3, 3, 13, 21, 19, 3, -7, -9, -5, -3, -3, -1}, {0, 1, 2, 4, 12, 42, 138, 414, 1235, 3764, 11604, 35664, 109132}, 30] (* Harvey P. Dale, Dec 27 2015 *)
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PROG
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(PARI) concat(0, Vec(x*(x^6 +x^5 -x^4 -x^3 -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 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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