A088972 Triangle read by rows: colored polyominoes. For n >= 1, 1 <= k <= n, T(n, k) is the number of k-colored n-celled polyominoes, counted up to rotation, reflection and permutation of the colors. Adjacent cells must be different colors. T(n, k) counts only polyominoes that include all k colors.

1, 0, 1, 0, 2, 2, 0, 5, 10, 5, 0, 12, 66, 55, 12, 0, 35, 415, 695, 285, 35, 0, 108, 2844, 8227, 6080, 1446, 108, 0, 369, 19875, 95697, 113418, 46441, 7140, 369, 0, 1285, 142046, 1092358, 1964647, 1238196, 320074, 34385, 1285, 0, 4655, 1026197, 12351464

Offset

1,5

Comments

For n > 1, T(n, 2) = T(n, n) = A000105(n).

Links

Table of n, a(n) for n=1..49.

D. Wasserman, Illustrations of colored pentominoes and hexominoes

Example

RBRG is considered the same as BRBG, but different from RBGR.
Triangle begins:
  1;
  0,   1;
  0,   2,     2;
  0,   5,    10,     5;
  0,  12,    66,    55,     12;
  0,  35,   415,   695,    285,   35;
  0, 108,  2844,  8227,   6080,  1446,  108;
  0, 369, 19875, 95697, 113418, 46441, 7140, 369;
  ...

Prog

(MATLAB) % See the link for MATLAB code.

Crossrefs

Cf. A000105.

Sequence in context: A396342 A321127 A222128 * A355570 A168505 A100334

Adjacent sequences: A088969 A088970 A088971 * A088973 A088974 A088975

Keyword

nonn,tabl

Author

David Wasserman, Oct 30 2003

Status

approved