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A325783
Reading the first row of this array, or the first column, or the successive antidiagonals is the same as reading this sequence.
2
1, 2, 2, 2, 3, 2, 2, 4, 5, 2, 3, 6, 7, 8, 3, 2, 9, 10, 11, 12, 2, 2, 13, 14, 15, 16, 17, 2, 4, 18, 19, 20, 21, 22, 23, 4, 5, 24, 25, 26, 27, 28, 29, 30, 5, 2, 31, 32, 33, 34, 35, 36, 37, 38, 2, 3, 39, 40, 41, 42, 43, 44, 45, 46, 47, 3, 6, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 6, 7, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 7, 8, 69
OFFSET
1,2
COMMENTS
The array is always extended by its antidiagonals with the smallest term not yet present that doesn't lead to a contradiction. The sequence is thus the lexicographically earliest of its kind.
This regular pattern appears: . . . . 3 . . 4 5 . . 6 7 8 . . 9 10 11 12 . . 13 14 15 16 17 . . 18 19 20 21 22 23 . . This is the first time that these terms appear in the sequence. So it is possible to calculate the terms of this pattern. - Bernard Schott, Jun 03 2019
FORMULA
a(n*(n+1)/2) = a(n*(n-1)/2+1) = a(n). - Rémy Sigrist, May 21 2019
T(n+1,k+1) = A000027(n,k) + 2 if both sequences are read as square arrays. - Charlie Neder, Jun 03 2019
From Bernard Schott, Jun 03 2019: (Start)
For 2 <= q <= k:
a(k*(k+1)/2 + 2) = (k-2)*(k-1)/2 + 3.
a(k*(k+1)/2 + q) = (k-2)*(k-1)/2 + q + 1.
a(k*(k+1)/2 + k) = a(k*(k+3)/2) = (k-2)*(k-1)/2 + k + 1 = (k^2-k+4)/2. (End)
EXAMPLE
Array:
1 2 2 2 3 2 2 4 5 2 3 ...
2 3 4 6 9 13 18 24 31 39 48 ...
2 5 7 10 14 19 25 32 40 49 59 ...
2 8 11 15 20 26 33 41 50 60 71 ...
3 12 16 21 27 34 42 51 61 72 84 ...
2 17 22 28 35 43 52 62 73 85 98 ...
2 23 29 36 44 53 63 74 86 99 113 ...
4 30 37 45 54 61 75 87 100 112 129 ...
5 38 46 55 62 76 88 101 113 130 146 ...
2 47 56 63 77 89 102 114 131 147 164 ...
3 57 64 78 90 101 115 132 148 165 183 ...
...
CROSSREFS
Cf. A325784 and A325785 where the same idea is developped, but restricted to, respectively, the first row and the first column of the arrays presented.
Sequence in context: A142240 A284565 A227911 * A048288 A050677 A058013
KEYWORD
nonn,tabl
AUTHOR
Eric Angelini, May 21 2019
STATUS
approved