cp's OEIS Frontend

A239075 Number of self-inverse permutations p on [n] with displacement of elements restricted by 3: |p(i)-i| <= 3.

%I A239075 #20 Mar 06 2024 04:53:47
%S A239075 1,1,2,4,10,22,48,103,225,492,1076,2348,5124,11184,24417,53305,116366,
%T A239075 254024,554534,1210554,2642656,5768943,12593649,27492040,60015368,
%U A239075 131014088,286004920,624351264,1362964321,2975363169,6495244138,14179175436,30953265426
%N A239075 Number of self-inverse permutations p on [n] with displacement of elements restricted by 3: |p(i)-i| <= 3.
%C A239075 Column k=3 of A238888.
%C A239075 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
%H A239075 Joerg Arndt and Alois P. Heinz, <a href="/A239075/b239075.txt">Table of n, a(n) for n = 0..1000</a>
%F A239075 G.f.: -(x-1)/(x^7-2*x^4-2*x+1).
%p A239075 gf:= -(x-1)/(x^7-2*x^4-2*x+1):
%p A239075 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A239075 seq(a(n), n=0..40);
%t A239075 CoefficientList[Series[(1 - x)/(x^7 - 2 x^4 - 2 x + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 12 2014 *)
%Y A239075 Cf. A000085, A238888.
%K A239075 nonn,easy
%O A239075 0,3
%A A239075 _Joerg Arndt_ and _Alois P. Heinz_, Mar 10 2014