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A363005 Number of sequences of n distinct integers whose Gilbreath transform is (1, 1, ..., 1). 4
1, 1, 2, 4, 12, 56, 416, 4764, 84272, 2278740, 92890636, 5659487836 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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Last modified February 27 14:46 EST 2024. Contains 370376 sequences. (Running on oeis4.)