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

1,6

Links

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

Example

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, ...
  ...| ...

Crossrefs

Cf. A001477 (row 1), A051162 (row 2, when read by rows), A070770 (row 3), A070771 (row 4), A070772 (row 5).

Sequence in context: A352515 A181347 A014587 * A025658 A025673 A025688

Adjacent sequences: A354385 A354386 A354387 * A354389 A354390 A354391

Keyword

nonn,tabl

Author

Peter Kagey, May 24 2022

Status

approved