%I A094170
%S A094170 0,0,1,10,33,88,187,360,625,1024,1581,2350,3361,4680,6343,8428,10977,
%T A094170 14080,17785,22194,27361,33400,40371,48400,57553,67968,79717,92950,
%U A094170 107745,124264,142591
%N A094170 Number of quasi-triominoes in an n X n bounding box.
%C A094170 A quasi-polyomino is a polyomino whose cells are not necessarily connected. 
               For all m > 1 there are an infinite number of quasi-m-ominoes; a(n) 
               counts the quasi-triomino (quasi-3-omino) equivalence classes (under 
               translation, rotation by 90 degrees and vertical and horizontal symmetry) 
               whose members fit into an n X n bounding box.
%C A094170 This is different from A082966 because that sequence considers these 
               two (for example) as different ways of placing 3 counters on a 3 
               X 3 checkerboard:
%C A094170 ---
%C A094170 -X-
%C A094170 X-X
%C A094170 and
%C A094170 -X-
%C A094170 X-X
%C A094170 ---
%C A094170 whereas here they are the same quasi-polyomino.
%C A094170 a(n) can also be interpreted as the number of non-equivalent Game of 
               Life patterns on an n X n board that have exactly 3 live cells, etc.
%H A094170 Erich Friedman, <a href="a094170.gif">Illustration of initial terms</
               a>
%F A094170 (1/32) [6n^4 - 12n^3 + 32n^2 - 58n + 29 - (6n-3)(-1)^n ]. - Ralf Stephan, 
               Dec 03 2004
%e A094170 Illustration of a(3), the 10 quasi-triominoes that fit into a 3 X 3 bounding 
               box:
%e A094170 XXX -XX XX- X-X X-X XX- X-X X-X X-- X--
%e A094170 --- -X- --X X-- -X- --- --- --- -X- --X
%e A094170 --- --- --- --- --- --X X-- -X- --X -X-
%Y A094170 Cf. A094171, A094172.
%Y A094170 Sequence in context: A162433 A003012 A020478 this_sequence A004638 A020479 
               A140866
%Y A094170 Adjacent sequences: A094167 A094168 A094169 this_sequence A094171 A094172 
               A094173
%K A094170 nonn
%O A094170 0,4
%A A094170 Jon Wild (wild(AT)music.mcgill.ca), May 07 2004
%E A094170 Corrected and extended by Jon Wild (wild(AT)music.mcgill.ca), May 11 
               2004