A391192 Triangle read by rows: T(n,k) is the number of free polyaboloes (or polytans) with n cells (counted as in A390996) of which k are square cells consisting of two triangles sharing a hypotenuse, 0 <= k <= n.

1, 1, 1, 2, 1, 1, 3, 7, 4, 2, 6, 19, 31, 14, 5, 7, 61, 137, 138, 54, 12, 13, 149, 580, 860, 643, 211, 35, 18, 362, 1989, 4539, 5020, 2939, 839, 108, 31, 795, 6266, 19877, 31906, 27674, 13457, 3352, 369, 45, 1704, 17776, 76905, 167972, 205684, 146725, 60860, 13472, 1285

Offset

0,4

Comments

T(0,0)=1 is included to make the triangular array regular.

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = A391191(n+k,k).

T(n,0) = A390885(n).

T(n,n) = A000105(n).

Example

Triangle begins:
  n\k|  0    1     2     3      4      5      6     7     8    9
  ---+----------------------------------------------------------
  0  |  1
  1  |  1    1
  2  |  2    1     1
  3  |  3    7     4     2
  4  |  6   19    31    14      5
  5  |  7   61   137   138     54     12
  6  | 13  149   580   860    643    211     35
  7  | 18  362  1989  4539   5020   2939    839   108
  8  | 31  795  6266 19877  31906  27674  13457  3352   369
  9  | 45 1704 17776 76905 167972 205684 146725 60860 13472 1285

Crossrefs

Antidiagonals are rows of A391191.

Cf. A000105, A390885, A390996 (row sums), A391193.

Sequence in context: A228904 A144512 A159314 * A361707 A135701 A051467

Adjacent sequences: A391189 A391190 A391191 * A391193 A391194 A391195

Keyword

nonn,tabl

Author

Pontus von Brömssen, Dec 08 2025

Status

approved