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Search: id:A094170
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| A094170 |
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Number of quasi-triominoes in an n X n bounding box. |
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+0
4
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| 0, 0, 1, 10, 33, 88, 187, 360, 625, 1024, 1581, 2350, 3361, 4680, 6343, 8428, 10977, 14080, 17785, 22194, 27361, 33400, 40371, 48400, 57553, 67968, 79717, 92950, 107745, 124264, 142591
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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.
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:
---
-X-
X-X
and
-X-
X-X
---
whereas here they are the same quasi-polyomino.
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.
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LINKS
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Erich Friedman, Illustration of initial terms
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FORMULA
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(1/32) [6n^4 - 12n^3 + 32n^2 - 58n + 29 - (6n-3)(-1)^n ]. - Ralf Stephan, Dec 03 2004
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EXAMPLE
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Illustration of a(3), the 10 quasi-triominoes that fit into a 3 X 3 bounding box:
XXX -XX XX- X-X X-X XX- X-X X-X X-- X--
--- -X- --X X-- -X- --- --- --- -X- --X
--- --- --- --- --- --X X-- -X- --X -X-
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CROSSREFS
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Cf. A094171, A094172.
Sequence in context: A162433 A003012 A020478 this_sequence A004638 A020479 A140866
Adjacent sequences: A094167 A094168 A094169 this_sequence A094171 A094172 A094173
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KEYWORD
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nonn
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AUTHOR
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Jon Wild (wild(AT)music.mcgill.ca), May 07 2004
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EXTENSIONS
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Corrected and extended by Jon Wild (wild(AT)music.mcgill.ca), May 11 2004
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