A364928 List of free corner-connected polyominoes in binary code (as defined in A246521), ordered first by number of bits, then by value of the binary code.

1, 6, 25, 56, 57, 198, 390, 452, 960, 454, 962, 2105, 3097, 3128, 4153, 7185, 10296, 14353, 15392, 31744, 65988, 966, 3129, 6201, 7193, 7217, 7224, 10297, 11320, 14361, 14392, 15377, 15400, 15408, 31752, 31760, 65990, 66498, 66500, 98502, 98756, 99264

Offset: 1

Author

Pontus von Brömssen, Aug 13 2023

Keywords

• nonn
• tabf

Comments

Corner-connected polyominoes are in one-to-one correspondence with ordinary polyominoes, but their binary codes differ and the order in which they appear here is different from that in A246521. The first size for which the order differs from A246521 is 4 (tetrominoes). Here the order of the tetrominoes is (T, S, square, L, straight), whereas in A246521 it is (L, square, T, S, straight).

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

Examples

			As irregular triangle:
   1;
   6;
  25,  56;
  57, 198, 390, 452, 960;
  ...
The corner-connected trominoes are oriented as follows to obtain their binary codes (see A246521):
  . . .   5 . .
  . 4 .   . 4 .
  0 . 3   . . 3
This gives the binary codes 2^0+2^3+2^4 = 25 and 2^3+2^4+2^5 = 56, respectively.
Similarly, for the corner-connected tetrominoes, the orientations
  . . . .   . . . .   . . . .   . . . .   9 . . .
  5 . . .   . . . .   . 8 . .   . 8 . .   . 8 . .
  . 4 . .   2 . 7 .   2 . 7 .   2 . 7 .   . . 7 .
  0 . 3 .   . 1 . 6   . 1 . .   . . . 6   . . . 6
give the binary codes 57, 198, 390, 452, 960, respectively.
		

Crossrefs

Cf. A000105, A246521.