A354388 Table read upward by antidiagonals: the n-th row gives the sums of each weakly decreasing nonnegative integer sequence of length n, listed in lexicographic order.
0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 2, 4, 0, 1, 2, 3, 3, 5, 0, 1, 2, 3, 2, 4, 6, 0, 1, 2, 3, 4, 3, 3, 7, 0, 1, 2, 3, 4, 2, 4, 4, 8, 0, 1, 2, 3, 4, 5, 3, 4, 5, 9, 0, 1, 2, 3, 4, 5, 2, 4, 5, 6, 10, 0, 1, 2, 3, 4, 5, 6, 3, 5, 6, 4, 11, 0, 1, 2, 3, 4, 5, 6, 2
Offset: 1
Examples
For n = 3, the weakly decreasing nonnegative integer sequences of length 3 listed in lexicographic order are (0,0,0), (1,0,0), (1,1,0), (1,1,1), (2,0,0), (2,1,0), (2,1,1), .... The sums of these sequences correspond to row 3. The table begins: 1 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ... 2 | 0, 1, 2, 2, 3, 4, 3, 4, 5, 6, 4, 5, 6, 7, 8, ... 3 | 0, 1, 2, 3, 2, 3, 4, 4, 5, 6, 3, 4, 5, 5, 6, ... 4 | 0, 1, 2, 3, 4, 2, 3, 4, 5, 4, 5, 6, 6, 7, 8, ... 5 | 0, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 4, 5, 6, 7, ... 6 | 0, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 4, 5, ... 7 | 0, 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, ... 8 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, ... 9 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, ... 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, ... 11 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 3, 4, ... 12 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 3, ... ...| ...
Links
- Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)