The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A284592 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A284592

Square array read by antidiagonals: T(n,k) is the number of pairs of partitions of n and k respectively, such that the pair of partitions have no part in common.
(history; published version)

#30 by Susanna Cuyler at Thu Jun 10 07:41:36 EDT 2021

STATUS

reviewed

approved

#29 by Joerg Arndt at Thu Jun 10 04:59:07 EDT 2021

STATUS

proposed

reviewed

#28 by Michel Marcus at Thu Jun 10 04:28:27 EDT 2021

STATUS

editing

proposed

#27 by Michel Marcus at Thu Jun 10 04:28:18 EDT 2021

NAME

Square array read by antidiagonals: T(n,k) is the the number of pairs of partitions of n and k respectively, such that the pair of partitions have no part in common.

STATUS

approved

editing

#26 by Peter Luschny at Mon Jun 07 04:51:38 EDT 2021

STATUS

reviewed

approved

#25 by Joerg Arndt at Mon Jun 07 04:11:33 EDT 2021

STATUS

proposed

reviewed

#24 by Joerg Arndt at Mon Jun 07 04:11:25 EDT 2021

STATUS

editing

proposed

#23 by Joerg Arndt at Mon Jun 07 04:11:21 EDT 2021

NAME

Square array read by antidiagonals: T(n,k) = is the the number of pairs of partitions of n and k respectively, such that the pair of partitions have no part in common.

STATUS

proposed

editing

#22 by Jean-François Alcover at Mon Jun 07 03:11:13 EDT 2021

STATUS

editing

proposed

#21 by Jean-François Alcover at Mon Jun 07 03:11:07 EDT 2021

MATHEMATICA

b[n_, k_, i_] := b[n, k, i] = If[n == 0 &&

(k == 0 || i == 1), 1, If[i < 1, 0, b[n, k, i - 1] +

Sum[b[Sequence @@ Sort[{n - i*j, k}], i - 1], {j, 1, n/i}] +

Sum[b[Sequence @@ Sort[{n, k - i*j}], i - 1], {j, 1, k/i}]]];

A[n_, k_] := Function [l, b[l[[1]], l[[2]], l[[2]]]][Sort[{n, k}]];

Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Jun 07 2021, after Alois P. Heinz *)

STATUS

approved

editing