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A365970
Triangle read by rows: T(n,k) is the number of generalized polyforms on the tetrahedral-octahedral honeycomb with n cells, k of which are octahedra; 0 <= k <= n.
1
1, 1, 1, 0, 1, 0, 0, 3, 1, 0, 0, 3, 5, 1, 0, 0, 6, 24, 13, 1, 0, 0, 3, 74, 105, 13, 0, 0, 0, 3, 169, 727, 276, 11, 0, 0, 0, 1, 285, 3223, 3440, 432, 4, 0, 0, 0, 1, 356, 10853, 27632, 10141, 459, 2, 0, 0, 0, 0, 344, 27198, 155524, 134527, 19597, 314, 0, 0, 0
OFFSET
0,8
COMMENTS
Polyforms are "free" in that they are counted up to rotation and reflection.
Conjecture: Columns and antidiagonals are unimodal.
Rows sums are given by A343909.
FORMULA
T(n,k) = 0 for k > n - floor((n - 1)/4).
EXAMPLE
Triangle begins:
1;
1, 1;
0, 1, 0;
0, 3, 1, 0;
0, 3, 5, 1, 0;
0, 6, 24, 13, 1, 0;
0, 3, 74, 105, 13, 0, 0;
0, 3, 169, 727, 276, 11, 0, 0;
0, 1, 285, 3223, 3440, 432, 4, 0, 0;
0, 1, 356, 10853, 27632, 10141, 459, 2, 0, 0;
0, 0, 344, 27198, 155524, 134527, 19597, 314, 0, 0, 0.
CROSSREFS
Cf. A343909.
Sequence in context: A345371 A306268 A354490 * A144357 A122848 A272481
KEYWORD
nonn,tabl,hard
AUTHOR
Peter Kagey, Sep 23 2023
STATUS
approved