A363003 - OEIS

%I #9 May 13 2023 13:48:09

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

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

%C 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).

%C Negative terms are permitted.

%e 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.

%e   (1, 2, 0, -4),

%e   (1, 2, 0, -2),

%e   (1, 2, 0,  0),

%e   (1, 2, 0,  2),

%e   (1, 2, 0,  4),

%e   (1, 2, 2,  0),

%e   (1, 2, 2,  2),

%e   (1, 2, 2,  4),

%e   (1, 2, 4,  0),

%e   (1, 2, 4,  2),

%e   (1, 2, 4,  4),

%e   (1, 2, 4,  6),

%e   (1, 2, 4,  8).

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

%K nonn,more

%O 0,3

%A _Pontus von Brömssen_, May 13 2023