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A260074
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Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by two: p(i)<>i and (i-p(i) mod n <= 2 or p(i)-i mod n <= 2).
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11
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1, 0, 1, 2, 9, 44, 80, 144, 260, 448, 808, 1456, 2640, 4788, 8744, 16016, 29444, 54268, 100304, 185824, 344996, 641664, 1195400, 2230176, 4165904, 7790244, 14581640, 27316240, 51209124, 96060300, 180291280, 338538480, 635940356, 1195021888, 2246289704
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OFFSET
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0,4
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-1,-4,3,-1,2,1,-1).
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FORMULA
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G.f.: -(27*x^14 -13*x^13 -61*x^12 -4*x^11 -70*x^10 +50*x^9 +44*x^8 +10*x^7 +38*x^6 -24*x^5 -6*x^4 +2*x^3 -3*x^2 +3*x-1) / ((x-1) *(x+1) *(x^2+1) *(x^2+x-1) *(x^4-2*x^3+x^2-2*x+1)).
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EXAMPLE
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a(6) = 80: 214365, 214635, 215364, 215634, 231564, 231645, 234561, 234615, 235614, 235641, 241365, 241635, 245361, 245631, 261345, 261534, 264315, 264531, 265314, 265341, 312564, 312645, 314265, 314562, 315264, 315642, 341265, 341562, 342561, 342615, 345261, 345612, 361245, 361542, 362514, 362541, 364215, 364512, 365214, 365241, 512364, 512634, 514362, 514632, 531264, 531642, 532614, 532641, 534261, 534612, 541362, 541632, 542361, 542631, 561234, 561342, 562314, 562341, 564231, 564312, 612345, 612534, 614235, 614532, 615234, 615342, 631245, 631542, 632514, 632541, 634215, 634512, 635214, 635241, 641235, 641532, 642315, 642531, 645231, 645312.
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MAPLE
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gf:= -(27*x^14 -13*x^13 -61*x^12 -4*x^11 -70*x^10 +50*x^9 +44*x^8 +10*x^7 +38*x^6 -24*x^5 -6*x^4 +2*x^3 -3*x^2 +3*x-1) / ((x-1) *(x+1) *(x^2+1) *(x^2+x-1) *(x^4-2*x^3+x^2-2*x+1)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);
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MATHEMATICA
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LinearRecurrence[{3, -2, 1, -1, -4, 3, -1, 2, 1, -1}, {1, 0, 1, 2, 9, 44, 80, 144, 260, 448, 808, 1456, 2640, 4788, 8744}, 50] (* Harvey P. Dale, Jul 15 2019 *)
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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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STATUS
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approved
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