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.
Original entry on oeis.org
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
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, ...
...
A360335
Array read by antidiagonals downwards: A(n,m) = number of set partitions of [2n] into 2-element subsets {i, i+k} with 1 <= k <= m.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 7, 5, 1, 1, 3, 12, 16, 8, 1, 1, 3, 15, 35, 38, 13, 1, 1, 3, 15, 63, 105, 89, 21, 1, 1, 3, 15, 90, 226, 329, 209, 34, 1, 1, 3, 15, 105, 417, 841, 1014, 491, 55, 1, 1, 3, 15, 105, 645, 1787, 3251, 3116, 1153, 89, 1
Offset: 1
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 3, 3, 3, 3, 3, 3, ...
1, 3, 7, 12, 15, 15, 15, 15, 15, ...
1, 5, 16, 35, 63, 90, 105, 105, 105, ...
1, 8, 38, 105, 226, 417, 645, 840, 945, ...
1, 13, 89, 329, 841, 1787, 3348, 5445, 7665, ...
1, 21, 209, 1014, 3251, 7938, 16717, 31647, 53250, ...
1, 34, 491, 3116, 12483, 36500, 86311, 180560, 344403, ...
1, 55, 1153, 9610, 47481, 167631, 459803, 1062435, 2211181, ...
...
A334250
Number of set partitions of [3n] into 3-element subsets {i, i+k, i+2k} with 1<=k<=n.
Original entry on oeis.org
1, 1, 2, 4, 12, 35, 129, 567, 2920, 16110, 103467, 717608, 5748214, 47937957, 441139750, 4319093093, 45963368076, 510202534002, 6150655137844, 76789781005325, 1028853084775725, 14294680087131380
Offset: 0
a(2) = 2: 123|456, 135|246.
a(3) = 4: 123|456|789, 123|468|579, 135|246|789, 147|258|369.
-
b:= proc(s, t) option remember; `if`(s={}, 1, (m-> add(
`if`({m-j, m-2*j} minus s={}, b(s minus {m, m-j, m-2*j},
t), 0), j=1..min(t, iquo(m-1, 2))))(max(s)))
end:
a:= proc(n) option remember; forget(b): b({$1..3*n}, n) end:
seq(a(n), n=0..12);
-
b[s_List, t_] := b[s, t] = If[s == {}, 1, Function[m, Sum[If[{m - j, m - 2j} ~Complement~ s == {}, b[s ~Complement~ {m, m - j, m - 2j}, t], 0], {j, 1, Min[t, Quotient[m - 1, 2]]}]][Max[s]]];
a[n_] := a[n] = b[Range[3n], n];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 12}] (* Jean-François Alcover, May 10 2020, after Maple *)
Showing 1-3 of 3 results.
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