A363003 Number of integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1).

1, 1, 2, 6, 26, 166, 1562, 21614, 438594, 13032614, 566069882

Offset: 0

Author

Pontus von Brömssen, May 13 2023

Keywords

• nonn
• more

Comments

a(n) is even for all n >= 2, because if the sequence (x_1, ..., x_n) has Gilbreath transform (1, ..., 1), so has the sequence (2 - x_1, ..., 2 - x_n).

Negative terms are permitted.

Examples

			For n = 4, the following 13 sequences, together with the sequences obtained by replacing each term x by 2-x in each of these sequences, have Gilbreath transform (1, 1, 1, 1), so a(4) = 26.
  (1, 2, 0, -4),
  (1, 2, 0, -2),
  (1, 2, 0,  0),
  (1, 2, 0,  2),
  (1, 2, 0,  4),
  (1, 2, 2,  0),
  (1, 2, 2,  2),
  (1, 2, 2,  4),
  (1, 2, 4,  0),
  (1, 2, 4,  2),
  (1, 2, 4,  4),
  (1, 2, 4,  6),
  (1, 2, 4,  8).
		

Crossrefs

Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363004 (distinct positive integers), A363005 (distinct integers).