

A246521


List of free polyominoes in binary coding, ordered by number of bits, then value of the binary code. Can be read as irregular table with row lengths A000105.


3



0, 1, 3, 7, 11, 15, 23, 27, 30, 75, 31, 47, 62, 79, 91, 94, 143, 181, 182, 188, 406, 1099, 63, 95, 111, 126, 159, 175, 183, 189, 190, 207, 219, 221, 222, 252, 347, 350, 378, 407, 413, 476, 504, 1103, 1115, 1118, 1227, 1244, 2127, 2229, 2230, 2236, 2292, 2451, 2454, 2460, 33867, 127
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OFFSET

1,3


COMMENTS

The binary coding (as suggested in a post to the SeqFan list by F. T. AdamsWatters) is obtained by summing the powers of 2 corresponding to the numbers covered by the polyomino, when the points of the quarterplane are numbered by antidiagonals, and the animal is placed (and flipped/rotated) as to obtain the smallest possible value, which in particular implies pushing it to both borders. See example for further details.
The smallest value for an nomino is the sum 2^0 + ... + 2^(n1) = 2^n  1 = A000225(n), and the largest value, obtained for the straight nomino, is 2^0 + 2^1 + 2^3 + ... + 2^A000217(n1) = A181388(n1).
See A246533 for the variant that lists fixed polyominoes.


LINKS

John Mason, Table of n, a(n) for n = 1..87147
F. T. AdamsWatters, Re: Sequence proposal by John Mason, SeqFan list, Aug 24 2014


EXAMPLE

Number the points of the first quadrant as follows:
...
9 ...
5 8 ...
2 4 7 ...
0 1 3 6 10 ...
The "empty" 0omino is represented by the empty sum equal to 0 = a(1).
The monomino is represented by a square on 0, and the binary code 2^0 = 1 = a(2).
The free domino is rotated to the ".." configuration represented by 2^0 + 2^1 (since this is smaller than the ":" configuration with value 2^0 + 2^2).
The A000105(3) = 2 free triominoes are represented by 2^0 + 2^1 + 2^3 (...) and 2^0 + 2^1 + 2^2 (:.). The latter value is smaller, therefore the Lshaped triomino is listed before the straight one.


CROSSREFS

See A246533 and A246559 for enumerations of fixed and onesided polyominoes.
Sequence in context: A071849 A165197 A246559 * A160785 A095100 A036994
Adjacent sequences: A246518 A246519 A246520 * A246522 A246523 A246524


KEYWORD

nonn


AUTHOR

M. F. Hasler, Aug 28 2014


EXTENSIONS

More terms from John Mason, Aug 29 2014


STATUS

approved



