[seqfan] First difference of lexigraphical ordering of subsets of integers

[Tommaso Martino]

Hello seqfans,
this is my first attempt, so I hope to not get in wrong.

Given S={1,2,3,4,5,6,7,8,9}, we can generate a finite sequence containing the lexicographical ordering of the subsets of k elements of S.
We now define the new sequence a(n) as the first difference of such list, which is a(n+1)-a(n).

-- Example 1.
Given S, the lexicographical ordering on the subsets of 2 elements of S is:

  12 13 14 15 16 17 18 19 23 24 25
  26 27 28 29 34 35 36 37 38 39 45
  46 47 48 49 56 57 58 59 67 68 69
  78 79 89

The first difference of the generated sequence is:

  1  1  1  1  1  1  1  4
  1  1  1  1  1  1  5
  1  1  1  1  1  6
  1  1  1  1  7
  1  1  1  8
  1  1  9
  1  10

-- Example 2.
Given S, the lexicographical ordering on the subsets of 3 elements of S is:

  123 124 125 126 127 128 129 134 135 136 137 138 139 145 146 147 148 149
  156 157 158 159 167 168 169 178 179 189 234 235 236 237 238 239 245 246
  247 248 249 256 257 258 259 267 268 269 278 279 289 345 346 347 348 349
  356 357 358 359 367 368 369 378 379 389 456 457 458 459 467 468 469 478
  479 489 567 568 569 578 579 589 678 679 689 789

The first difference of the generated sequence is:

  1   1   1   1   1   1
  5   1   1   1   1   1
  6   1   1   1   1   7
  1   1   1   8   1   1
  9   1  10  45   1   1
  1   1   1   6   1   1
  1   1   7   1   1   1
  8   1   1   9   1  10
  56  1   1   1   1   7
  1   1   1   8   1   1
  9   1  10  67   1   1
  1   8   1   1   9   1
  10  78  1   1   9   1
  10  89  1  10 100

Some repeating pattern seems to appear in the sequence.
Different sequences can be generated with the same S, and increasing values of k < S.
The length of the sequence can be easily computed, and it is a function of both k and S.
Modifying the length of S, for example S={2..8}, different sequences can be obtained.

Is it worth submitting to OEIS?

Thank you,
Tommaso MARTINO