A393392 Array read by antidiagonals: T(n,k) is the number of free (r,s)-polyleapers with k cells, where r = A094192(n-1) and s = A094193(n-1) if n > 1, (r,s) = (1,0) if n = 1; n, k >= 1.

1, 1, 1, 2, 1, 1, 5, 6, 1, 1, 12, 35, 6, 1, 1, 35, 290, 35, 6, 1, 1, 108, 2680, 290, 35, 6, 1, 1, 369, 26379, 2714, 290, 35, 6, 1, 1, 1285, 267598, 27524, 2714, 290, 35, 6, 1, 1, 4655, 2758016, 291073, 27524, 2714, 290, 35, 6, 1, 1

Offset

1,4

Comments

See A393390 for details.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..91 (first 13 antidiagonals)

Formula

T(m,k) = T(n,k) if k < 2*min(p+q,r+s), where (p,q) and (r,s) are the leap sizes corresponding to rows m and n, respectively.

Example

Array begins:
    |       | k
  n | (r,s) | 1  2  3  4   5    6     7      8       9       10
  --+-------+--------------------------------------------------
  1 | (1,0) | 1  1  2  5  12   35   108    369    1285     4655
  2 | (2,1) | 1  1  6 35 290 2680 26379 267598 2758016 28749456
  3 | (3,2) | 1  1  6 35 290 2714 27524 291073 3166124 35169275
  4 | (4,1) | 1  1  6 35 290 2714 27524 291073 3166124 35173508
  5 | (4,3) | 1  1  6 35 290 2714 27524 291073 3166124 35174903
  6 | (5,2) | 1  1  6 35 290 2714 27524 291073 3166124 35174903
  7 | (5,4) | 1  1  6 35 290 2714 27524 291073 3166124 35174903

Crossrefs

Rows 1-5 are A000105 (polyominoes), A030446 (polyknights), A093989 (polyzebras), A393838 (polygiraffes), A394196 (polyantelopes).

Cf. A094192, A094193, A393390 (fixed), A393391 (one-sided), A393393 (coordination sequences for the underlying leaper graphs).

Sequence in context: A326048 A156576 A293219 * A266572 A266681 A210664

Adjacent sequences: A393389 A393390 A393391 * A393393 A393394 A393395

Keyword

nonn,tabl

Author

Pontus von Brömssen, Feb 16 2026

Status

approved