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A239075
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Number of self-inverse permutations p on [n] with displacement of elements restricted by 3: |p(i)-i| <= 3.
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2
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1, 1, 2, 4, 10, 22, 48, 103, 225, 492, 1076, 2348, 5124, 11184, 24417, 53305, 116366, 254024, 554534, 1210554, 2642656, 5768943, 12593649, 27492040, 60015368, 131014088, 286004920, 624351264, 1362964321, 2975363169, 6495244138, 14179175436, 30953265426
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OFFSET
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0,3
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COMMENTS
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Also the number of compositions of n into m sorts of k's, where m=1 if k=1,2,3, m=2 if k>6 and m=3 if k=4,5,6. - Beimar Naranjo, Mar 05 2024
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LINKS
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FORMULA
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G.f.: -(x-1)/(x^7-2*x^4-2*x+1).
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MAPLE
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gf:= -(x-1)/(x^7-2*x^4-2*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[(1 - x)/(x^7 - 2 x^4 - 2 x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 12 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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STATUS
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approved
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