A363005 - OEIS

A363005

Number of sequences of n distinct integers whose Gilbreath transform is (1, 1, ..., 1).

1, 1, 2, 4, 12, 56, 416, 4764, 84272, 2278740, 92890636, 5659487836

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OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..11.

EXAMPLE

For n = 4, the following 6 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) = 12.

(1, 2, 0, -4),

(1, 2, 0, -2),

(1, 2, 0, 4),

(1, 2, 4, 0),

(1, 2, 4, 6),

(1, 2, 4, 8).

CROSSREFS

Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363003, A363004 (distinct positive integers).

Sequence in context: A158569 A020106 A099928 * A000568 A177921 A301481

Adjacent sequences: A363002 A363003 A363004 * A363006 A363007 A363008

KEYWORD

nonn,more

AUTHOR

Pontus von Brömssen, May 13 2023

STATUS

approved