cp's OEIS Frontend

A220622 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

%I A220622 #10 Jul 23 2025 01:18:35
%S A220622 1,22,125,1189,9176,76955,624227,5131406,41957895,343809419,
%T A220622 2814822600,23053276257,188779537161,1545969533334,12660108907789,
%U A220622 103675885828389,849017313171328,6952739324271787,56937068599653211,466266655043137726
%N A220622 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
%C A220622 Row 3 of A220621.
%H A220622 R. H. Hardin, <a href="/A220622/b220622.txt">Table of n, a(n) for n = 1..210</a>
%F A220622 Empirical: a(n) = 6*a(n-1) + 22*a(n-2) - 32*a(n-3) - 12*a(n-4) + 8*a(n-5) - 3*a(n-6).
%F A220622 Empirical g.f.: x*(1 + 16*x - 29*x^2 - 13*x^3 + 8*x^4 - 3*x^5) / (1 - 6*x - 22*x^2 + 32*x^3 + 12*x^4 - 8*x^5 + 3*x^6). - _Colin Barker_, Aug 01 2018
%e A220622 Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
%e A220622 ..6..4..0....0..6..4....0..7..0....0..0..0....6..4..0....0..7..0....0..7..0
%e A220622 ..0..0..0....0..6..4....3..6..4....0..0..0....9..9..0....3..6..4....3..0..7
%e A220622 ..0..0..0....6..4..0....0..6..4....0..6..4....0..1..1....0..0..0....0..3..0
%Y A220622 Cf. A220621.
%K A220622 nonn
%O A220622 1,2
%A A220622 _R. H. Hardin_, Dec 17 2012