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 1-6 of 6 results.

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

Views

Author

Peter Dolland, Feb 03 2023

Keywords

Examples

			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, ...
  ...

Crossrefs

Main diagonal is A014307.
Columns 1..4 are A000012, A000045(n+1), A052967, A320346.
Cf. A001147, A104443, A360333, A360334.

Formula

A(n,m) = A001147(n) = A104443(n,2) for m >= 2n - 1.

A337520 Number of set partitions of [4n] into 4-element subsets {i, i+k, i+2k, i+3k} with 1<=k<=n.

Original entry on oeis.org

1, 1, 2, 4, 10, 22, 64, 147, 409, 1092, 3253, 8661, 28585, 83190, 274001, 912373, 3366384, 13253582, 61533277, 290493694
Offset: 0

Views

Author

Alois P. Heinz, Nov 18 2020

Keywords

Examples

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

Links

Crossrefs

Cf. A000566, A014307, A104430, A334250.
Main diagonal of A360333.

Programs

  • Maple
    b:= proc(s, t) option remember; `if`(s={}, 1, (m-> add(
     `if`({seq(m-h*j, h=1..3)} minus s={}, b(s minus {seq(m-h*j,
      h=0..3)}, t), 0), j=1..min(t, iquo(m-1, 3))))(max(s)))
    end:
a:= proc(n) option remember; forget(b): b({$1..4*n}, n) end:
seq(a(n), n=0..12);
  • Mathematica
    b[s_, t_] := b[s, t] = If[s == {}, 1, Function[m, Sum[       If[Union@Table[m-h*j, {h, 1, 3}] ~Complement~ s == {}, b[s ~Complement~ Union@Table[m-h*j, {h, 0, 3}], t], 0], {j, 1, Min[t, Quotient[m-1, 3]]}]][Max[s]]];
a[n_] := a[n] = b[Range[4n], n];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 12}] (* Jean-François Alcover, Feb 13 2023, after Alois P. Heinz *)

A360334 Array read by antidiagonals downwards: A(n,m) = number of set partitions of [3n] into 3-element subsets {i, i+k, i+2k} 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, 5, 7, 8, 1, 1, 2, 5, 12, 13, 13, 1, 1, 2, 5, 15, 25, 24, 21, 1, 1, 2, 5, 15, 35, 56, 44, 34, 1, 1, 2, 5, 15, 46, 84, 126, 81, 55, 1, 1, 2, 5, 15, 55, 129, 211, 281, 149, 89, 1, 1, 2, 5, 15, 55, 185, 346, 537, 625, 274, 144, 1
Offset: 1

Views

Author

Peter Dolland, Feb 03 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,   5,    5,    5,    5,     5,     5, ...
  1,  5,   7,  12,   15,   15,   15,    15,    15, ...
  1,  8,  13,  25,   35,   46,   55,    55,    55, ...
  1, 13,  24,  56,   84,  129,  185,   232,   232, ...
  1, 21,  44, 126,  211,  346,  567,   831,  1040, ...
  1, 34,  81, 281,  537,  973, 1781,  2920,  4242, ...
  1, 55, 149, 625, 1352, 2732, 5643, 10213, 16110, ...
  ...

Crossrefs

Main diagonal is A334250.
Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Cf. A104429, A104443, A360333, A360335.

Formula

A(n,m) = A104429(n) = A104443(n,3) for m >= floor((3n - 1) / 2).

A360491 Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [5n] into 5-element subsets {i, i+k, i+2k, i+3k, i+4k} 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, 21, 43, 84, 81, 55, 1, 1, 2, 4, 10, 21, 58, 89, 180, 149, 89, 1, 1, 2, 4, 10, 21, 59, 120, 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,   21,   21,   21,   21, ...
  1,  13,  24,   41,   43,   58,   59,   59,   59, ...
  1,  21,  44,   84,   89,  120,  124,  125,  125, ...
  1,  34,  81,  180,  192,  280,  289,  344,  349, ...
  1,  55, 149,  372,  404,  626,  648,  759,  811, ...
  1,  89, 274,  785,  860, 1454, 1510, 1877, 1996, ...
  1, 144, 504, 1637, 1816, 3272, 3414, 4263, 4565, ...
  ...

Crossrefs

Main diagonal is A349430.
Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Cf. A104431, A104443, A360333..A360335, A360492, A360493.

Formula

A(n,m) = A104431(n) = A104443(n,5) for m >= floor((5n - 1) / 4).

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 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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