A107082 Put in lexicographic order and concatenate all sequences that start with 0 and have difference sequences that use the digits 1 through 9 in order.

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 0, 1, 3, 6, 10, 15, 21, 28, 117, 0, 1, 3, 6, 10, 15, 21, 99, 108, 0, 1, 3, 6, 10, 15, 21, 810, 0, 1, 3, 6, 10, 15, 82, 90, 99, 0, 1, 3, 6, 10, 15, 82, 171, 0, 1, 3, 6, 10, 15, 693, 702, 0, 1, 3, 6, 10, 15, 6804, 0, 1, 3, 6, 10, 66, 73, 81, 90, 0, 1, 3, 6

Offset

1,3

Comments

Sequence contains 1536 terms, including 336 distinct terms of which 147 appear exactly once. The 256 = 2^8 concatenated subsequences beginning with 0 have lengths 2 through 10, which occur 1, 8, 28, 56, 70, 56, 28, 8, 1 times, respectively, corresponding to C(8,k) = A007318(8,k), the number of ways 0 <= k <= 8 commas can be inserted between digits within "123456789". - Rick L. Shepherd, Feb 21 2013

References

Loosely based on a puzzle at Creative Thinking Puzzles.

Links

Rick L. Shepherd, Table of n, a(n) for n = 1..1536 (full sequence)

Creative Thinking Puzzles, A puzzle.

Joshua Zucker, The full sequence

Example

0, 1, 24, 28, 595, 684 will appear in this sequence because the difference sequence is 1, 23, 4, 567, 89.

Crossrefs

Cf. A107081 for the special case that inspired this.

Sequence in context: A108923 A033441 A338334 * A267238 A256379 A187845

Adjacent sequences: A107079 A107080 A107081 * A107083 A107084 A107085

Keyword

base,fini,full,nonn

Author

Joshua Zucker, May 11 2005

Status

approved