A360333 - OEIS

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.

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

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..66.

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).

Cf. A104430, A104443, A360334, A360335.

Sequence in context: A360493 A360492 A360491 * A047913 A152977 A360334

Adjacent sequences: A360330 A360331 A360332 * A360334 A360335 A360336

KEYWORD

nonn,tabl

AUTHOR

Peter Dolland, Feb 03 2023

STATUS

approved