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 A363003 Number of integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1). 5
 1, 1, 2, 6, 26, 166, 1562, 21614, 438594, 13032614, 566069882 (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 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

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Last modified November 29 06:17 EST 2023. Contains 367422 sequences. (Running on oeis4.)