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A360334
Array read by antidiagonals downwards: A(n,m) = number of set partitions of [3n] into 3-element subsets {i, i+k, i+2k} with 1 <= k <= m.
3
1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 5, 7, 8, 1, 1, 2, 5, 12, 13, 13, 1, 1, 2, 5, 15, 25, 24, 21, 1, 1, 2, 5, 15, 35, 56, 44, 34, 1, 1, 2, 5, 15, 46, 84, 126, 81, 55, 1, 1, 2, 5, 15, 55, 129, 211, 281, 149, 89, 1, 1, 2, 5, 15, 55, 185, 346, 537, 625, 274, 144, 1
OFFSET
1,5
FORMULA
A(n,m) = A104429(n) = A104443(n,3) for m >= floor((3n - 1) / 2).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 2, 2, 2, 2, 2, 2, 2, ...
1, 3, 4, 5, 5, 5, 5, 5, 5, ...
1, 5, 7, 12, 15, 15, 15, 15, 15, ...
1, 8, 13, 25, 35, 46, 55, 55, 55, ...
1, 13, 24, 56, 84, 129, 185, 232, 232, ...
1, 21, 44, 126, 211, 346, 567, 831, 1040, ...
1, 34, 81, 281, 537, 973, 1781, 2920, 4242, ...
1, 55, 149, 625, 1352, 2732, 5643, 10213, 16110, ...
...
CROSSREFS
Main diagonal is A334250.
Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Sequence in context: A360333 A047913 A152977 * A259799 A208447 A320750
KEYWORD
nonn,tabl
AUTHOR
Peter Dolland, Feb 03 2023
STATUS
approved