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A363003
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Number of integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1).
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5
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1, 1, 2, 6, 26, 166, 1562, 21614, 438594, 13032614, 566069882
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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).
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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