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A360333
Array read by antidiagonals downwards: A(n,m) = number of set partitions of [4n] into 4-element subsets {i, i+k, i+2k, i+3k} with 1 <= k <= m.
6
1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 4, 7, 8, 1, 1, 2, 4, 10, 13, 13, 1, 1, 2, 4, 11, 19, 24, 21, 1, 1, 2, 4, 11, 22, 41, 44, 34, 1, 1, 2, 4, 11, 23, 48, 84, 81, 55, 1, 1, 2, 4, 11, 23, 64, 101, 180, 149, 89, 1
OFFSET
1,5
FORMULA
A(n,m) = A104430(n) = A104443(n,4) for m >= floor((4n - 1) / 3).
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, 4, 4, 4, 4, 4, 4, ...
1, 5, 7, 10, 11, 11, 11, 11, 11, ...
1, 8, 13, 19, 22, 23, 23, 23, 23, ...
1, 13, 24, 41, 48, 64, 68, 68, 68, ...
1, 21, 44, 84, 101, 134, 147, 148, 161, ...
1, 34, 81, 180, 225, 318, 353, 409, 444, ...
1, 55, 149, 372, 485, 721, 814, 929, 1092, ...
...
CROSSREFS
Main diagonal is A337520.
Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Sequence in context: A360493 A360492 A360491 * A047913 A152977 A360334
KEYWORD
nonn,tabl
AUTHOR
Peter Dolland, Feb 03 2023
STATUS
approved