A363003 - OEIS

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

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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..10.

EXAMPLE

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).

Sequence in context: A005272 A307082 A178089 * A002449 A059430 A288607

Adjacent sequences: A363000 A363001 A363002 * A363004 A363005 A363006

KEYWORD

nonn,more

AUTHOR

Pontus von Brömssen, May 13 2023

STATUS

approved