A337972 -id:A337972 - cp's OEIS frontend

A338014 Triangular array read by rows: T(n,k) = A338012(n) + A338012(k) for 1 <= k <= n.

0, 3, 6, 4, 7, 8, 10, 13, 14, 20, 18, 21, 22, 28, 36, 23, 26, 27, 33, 41, 46, 34, 37, 38, 44, 52, 57, 68, 55, 58, 59, 65, 73, 78, 89, 110, 67, 70, 71, 77, 85, 90, 101, 122, 134, 93, 96, 97, 103, 111, 116, 127, 148, 160, 186, 95, 98, 99, 105, 113, 118, 129, 150, 162, 188, 190

Offset: 1

Peter Kagey, Oct 06 2020

			Addition table begins:
   + |  0  3  4 10 18 23  34  55  67
-----+-------------------------------
   0 |  0
   3 |  3  6
   4 |  4  7  8
  10 | 10 13 14 20
  18 | 18 21 22 28 36
  23 | 23 26 27 33 41 46
  34 | 34 37 38 44 52 57  68
  55 | 55 58 59 65 73 78  89 110
  67 | 67 70 71 77 85 90 101 122 134

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Cf. A338012, A338015 (by antidiagonals), A338016 (multiplication).

Cf. A337659, A337972.

A337973 Addition table from A337946, read by antidiagonals.

Original entry on oeis.org

2, 4, 4, 8, 6, 8, 13, 10, 10, 13, 23, 15, 14, 15, 23, 31, 25, 19, 19, 25, 31, 48, 33, 29, 24, 29, 33, 48, 62, 50, 37, 34, 34, 37, 50, 62, 86, 64, 54, 42, 44, 42, 54, 64, 86, 114, 88, 68, 59, 52, 52, 59, 68, 88, 114, 127, 116, 92, 73, 69, 60, 69, 73, 92, 116, 127

Offset: 1

Peter Kagey, Oct 05 2020

			Addition table for A337946 begins:
  +  |  1  3  7 12  22  30  47  61  85
-----+--------------------------------
   1 |  2  4  8 13  23  31  48  62  86
   3 |  4  6 10 15  25  33  50  64  88
   7 |  8 10 14 19  29  37  54  68  92
  12 | 13 15 19 24  34  42  59  73  97
  22 | 23 25 29 34  44  52  69  83 107
  30 | 31 33 37 42  52  60  77  91 115
  47 | 48 50 54 59  69  77  94 108 132
  61 | 62 64 68 73  83  91 108 122 146
  85 | 86 88 92 97 107 115 132 146 170

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened)

Cf. A337660, A337946, A338015, A338032.

Cf. A337972 (by rows), A337975 (multiplication).

A337974 Triangular array read by rows: T(n,k) = A337946(n) * A337946(k), for 1 <= k <= n.

Original entry on oeis.org

1, 3, 9, 7, 21, 49, 12, 36, 84, 144, 22, 66, 154, 264, 484, 30, 90, 210, 360, 660, 900, 47, 141, 329, 564, 1034, 1410, 2209, 61, 183, 427, 732, 1342, 1830, 2867, 3721, 85, 255, 595, 1020, 1870, 2550, 3995, 5185, 7225, 113, 339, 791, 1356, 2486, 3390, 5311, 6893, 9605, 12769

Offset: 1

Peter Kagey, Oct 05 2020

This sequence, A337947, and A337972 partition the positive integers.

			Multiplication table for A337946 begins:
  *  |  1   3   7   12   22   30   47   61   85
-----+-----------------------------------------
   1 |  1
   3 |  3   9
   7 |  7  21  49
  12 | 12  36  84  144
  22 | 22  66 154  264  484
  30 | 30  90 210  360  660  900
  47 | 47 141 329  564 1034 1410 2209
  61 | 61 183 427  732 1342 1830 2867 3721
  85 | 85 255 595 1020 1870 2550 3995 5185 7225

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Cf. A337661, A337946, A338016, A338033.

Cf. A337972 (addition table), A337975 (read by antidiagonals).

A338031 Triangular array read by rows: T(n,k) = A337656(n) + A337656(k) for 1 <= k <= n.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 10, 14, 12, 13, 15, 19, 24, 20, 21, 23, 27, 32, 40, 30, 31, 33, 37, 42, 50, 60, 44, 45, 47, 51, 56, 64, 74, 88, 65, 66, 68, 72, 77, 85, 95, 109, 130, 91, 92, 94, 98, 103, 111, 121, 135, 156, 182, 107, 108, 110, 114, 119, 127, 137, 151, 172, 198, 214

Offset: 1

Peter Kagey, Oct 07 2020

			Addition table begins:
   + |  0  1  3  7 12 20 30  44  65
-----+-----------------------------
   0 |  0
   1 |  1  2
   3 |  3  4  6
   7 |  7  8 10 14
  12 | 12 13 15 19 24
  20 | 20 21 23 27 32 40
  30 | 30 31 33 37 42 50 60
  44 | 44 45 47 51 56 64 74  88
  65 | 65 66 68 72 77 85 95 109 130

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Cf. A337656, A337657, A338032 (by antidiagonals), A338033 (multiplication).

Cf. A337659, A337972, A338014.

cp's OEIS Frontend

A338014 Triangular array read by rows: T(n,k) = A338012(n) + A338012(k) for 1 <= k <= n.

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A337973 Addition table from A337946, read by antidiagonals.

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A337974 Triangular array read by rows: T(n,k) = A337946(n) * A337946(k), for 1 <= k <= n.

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A338031 Triangular array read by rows: T(n,k) = A337656(n) + A337656(k) for 1 <= k <= n.

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