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

1,2

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.

Links

Table of n, a(n) for n=1..42.

Example

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.

Sequence in context: A165217 A320422 A075224 * A042185 A065069 A319429

Adjacent sequences: A364925 A364926 A364927 * A364929 A364930 A364931

Keyword

nonn,tabf

Author

Pontus von Brömssen, Aug 13 2023

Status

approved