cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A349430 Number of set partitions of [5n] into 5-element subsets {i, i+k, i+2k, i+3k, i+4k} with 1<=k<=n.

Original entry on oeis.org

1, 1, 2, 4, 10, 20, 58, 124, 344, 811, 2071, 4973, 15454, 36031, 96212, 237563, 668695, 1626751, 4674373, 11470722, 31460456, 81705943, 224598113
Offset: 0

Views

Author

Alois P. Heinz, Nov 17 2021

Keywords

Examples

			a(4) = 10: {{1,2,3,4,5}, {6,7,8,9,10}, {11,12,13,14,15}, {16,17,18,19,20}},
  {{1,3,5,7,9}, {2,4,6,8,10}, {11,12,13,14,15}, {16,17,18,19,20}},
  {{1,2,3,4,5}, {6,8,10,12,14}, {7,9,11,13,15}, {16,17,18,19,20}},
  {{1,4,7,10,13}, {2,5,8,11,14}, {3,6,9,12,15}, {16,17,18,19,20}},
  {{1,2,3,4,5}, {6,7,8,9,10}, {11,13,15,17,19}, {12,14,16,18,20}},
  {{1,3,5,7,9}, {2,4,6,8,10}, {11,13,15,17,19}, {12,14,16,18,20}},
  {{1,5,9,13,17}, {2,4,6,8,10}, {3,7,11,15,19}, {12,14,16,18,20}},
  {{1,2,3,4,5}, {6,9,12,15,18}, {7,10,13,16,19}, {8,11,14,17,20}},
  {{1,3,5,7,9}, {2,6,10,14,18}, {4,8,12,16,20}, {11,13,15,17,19}},
  {{1,5,9,13,17}, {2,6,10,14,18}, {3,7,11,15,19}, {4,8,12,16,20}}.

Links

Crossrefs

Cf. A000567 (number of subsets), A008587 (number of elements), A104431 (when k is unbounded), A337520.
Main diagonal of A360491.

Programs

  • Maple
    b:= proc(s, t) option remember; `if`(s={}, 1, (m-> add(
     `if`({seq(m-h*j, h=1..4)} minus s={}, b(s minus {seq(m-h*j,
      h=0..4)}, t), 0), j=1..min(t, iquo(m-1, 4))))(max(s)))
    end:
a:= proc(n) option remember; forget(b): b({$1..5*n}, n) end:
seq(a(n), n=0..10);
  • Mathematica
    b[s_, t_] := b[s, t] = If[s == {}, 1, Function[m, Sum[If[Union[Table[m - h*j, {h, 1, 4}] ~Complement~ s] == {}, b[s  ~Complement~ Union[Table[m - h*j, {h, 0, 4}]], t], 0], {j, 1, Min[t, Quotient[m-1, 4]]}]][Max[s]]];
a[n_] := a[n] = b[Range[5n], n];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 15}] (* Jean-François Alcover, May 16 2022, after Alois P. Heinz *)

Extensions

a(22) from Alois P. Heinz, Nov 23 2022

A360492 Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [6n] into 6-element subsets {i, i+k, i+2k, i+3k, i+4k, i+5k} 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, 10, 19, 24, 21, 1, 1, 2, 4, 10, 20, 41, 44, 34, 1, 1, 2, 4, 10, 20, 43, 84, 81, 55, 1, 1, 2, 4, 10, 20, 56, 89, 180, 149, 89, 1, 1, 2, 4, 10, 20, 57, 115, 192, 372, 274, 144, 1
Offset: 1

Views

Author

Peter Dolland, Feb 09 2023

Keywords

Examples

			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,   10,   10,   10,   10,    10, ...
  1,   8,  13,   19,   20,   20,   20,   20,    20, ...
  1,  13,  24,   41,   43,   56,   57,   57,    57, ...
  1,  21,  44,   84,   89,  115,  118,  119,   119, ...
  1,  34,  81,  180,  192,  267,  274,  328,   329, ...
  1,  55, 149,  372,  404,  592,  609,  718,   759, ...
  1,  89, 274,  785,  860, 1372, 1416, 1778,  1861, ...
  1, 144, 504, 1637, 1816, 3028, 3136, 3972,  4179, ...
  1, 233, 927, 3442, 3857, 7038, 7323, 9979, 10623, ...
  ...

Crossrefs

Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Cf. A104432, A104443, A360333..A360335, A360491, A360493.

Formula

A(n,m) = A104432(n) = A104443(n,6) for m >= floor((6n - 1) / 5).

A360493 Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [7n] into 7-element subsets {i, i+k, i+2k, i+3k, i+4k, i+5k, i+6k} 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, 10, 19, 24, 21, 1, 1, 2, 4, 10, 20, 41, 44, 34, 1, 1, 2, 4, 10, 20, 43, 84, 81, 55, 1, 1, 2, 4, 10, 20, 56, 89, 180, 149, 89, 1, 1, 2, 4, 10, 20, 56, 115, 192, 372, 274, 144, 1
Offset: 1

Views

Author

Peter Dolland, Feb 09 2023

Keywords

Examples

			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,   10,   10,   10,   10,    10, ...
  1,   8,  13,   19,   20,   20,   20,   20,    20, ...
  1,  13,  24,   41,   43,   56,   56,   56,    56, ...
  1,  21,  44,   84,   89,  115,  116,  117,   117, ...
  1,  34,  81,  180,  192,  267,  269,  322,   323, ...
  1,  55, 149,  372,  404,  592,  597,  704,   744, ...
  1,  89, 274,  785,  860, 1372, 1384, 1741,  1822, ...
  1, 144, 504, 1637, 1816, 3028, 3060, 3886,  4088, ...
  1, 233, 927, 3442, 3857, 7038, 7114, 9742, 10374, ...
  ...

Crossrefs

Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Cf. A104433, A104443, A360333..A360335, A360491, A360492.

Formula

A(n,m) = A104433(n) = A104443(n,7) for m >= floor((7*n - 1) / 6).
Showing 1-3 of 3 results.

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