cp's OEIS Frontend

A216796 Number of permutations of an n X 4 array with each element moving exactly one horizontally or vertically and without 2-loops.

%I A216796 #8 Feb 23 2018 11:53:18
%S A216796 0,6,8,88,292,1774,7676,39844,186996,927134,4460016,21812696,
%T A216796 105716132,514912230,2501152692,12167375908,59142175940,287602784246,
%U A216796 1398239939960,6798750327544,33055539575012,160722650037822,781448253270316
%N A216796 Number of permutations of an n X 4 array with each element moving exactly one horizontally or vertically and without 2-loops.
%C A216796 Column 4 of A216800.
%H A216796 R. H. Hardin, <a href="/A216796/b216796.txt">Table of n, a(n) for n = 1..210</a>
%F A216796 Empirical: a(n) = 4*a(n-1) +10*a(n-2) -28*a(n-3) -7*a(n-4) +30*a(n-5) -8*a(n-6).
%F A216796 Empirical g.f.: 2*x^2*(1 - 2*x)*(3 - 2*x - 6*x^2 + 2*x^3) / ((1 - x)*(1 - 3*x - 13*x^2 + 15*x^3 + 22*x^4 - 8*x^5)). - _Colin Barker_, Feb 23 2018
%e A216796 Some solutions for n=4:
%e A216796 ..4..0..3..7....4..0..3..7....1..2..3..7....1..5..3..7....4..0..1..2
%e A216796 ..5..1..2.11....5..1..2.11....0..9..5..6....0..4..2.11....8..6..7..3
%e A216796 .12..8..6.15....9.13..6.15....4.10.11.15....9.10..6.15...12..5.11.15
%e A216796 .13..9.10.14....8.12.10.14....8.12.13.14....8.12.13.14...13..9.10.14
%Y A216796 Cf. A216800.
%K A216796 nonn
%O A216796 1,2
%A A216796 _R. H. Hardin_, Sep 17 2012