A391191 Irregular triangle read by rows: T(n,k) is the number of free polyaboloes (or polytans) with n cells of which 2*k share a hypotenuse in pairs (making up k squares), 0 <= k <= n/2.

1, 1, 2, 1, 3, 1, 6, 7, 1, 7, 19, 4, 13, 61, 31, 2, 18, 149, 137, 14, 31, 362, 580, 138, 5, 45, 795, 1989, 860, 54, 76, 1704, 6266, 4539, 643, 12, 115, 3477, 17776, 19877, 5020, 211, 190, 6969, 47414, 76905, 31906, 2939, 35, 289, 13596, 118979, 267289, 167972, 27674, 839

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Formula

T(n,k) = A391192(n-k,k).

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

T(2*n,n) = A000105(n).

Example

Irregular triangle begins:
  n\k|  0    1    2    3   4  5
  ---+-------------------------
   0 |  1
   1 |  1
   2 |  2    1
   3 |  3    1
   4 |  6    7    1
   5 |  7   19    4
   6 | 13   61   31    2
   7 | 18  149  137   14
   8 | 31  362  580  138   5
   9 | 45  795 1989  860  54
  10 | 76 1704 6266 4539 643 12

Crossrefs

Rows are antidiagonals of A391192.

Cf. A000105, A006074 (row sums), A390885, A391193.

Sequence in context: A053222 A351159 A318762 * A262598 A370899 A191854

Adjacent sequences: A391188 A391189 A391190 * A391192 A391193 A391194

Keyword

nonn,tabf

Author

Pontus von Brömssen, Dec 08 2025

Status

approved