A349903 - OEIS

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A349903

Array read by ascending antidiagonals. Inverse Euler transform of the right-shifted k-bonacci numbers.

0, 0, 1, 0, 1, 0, 0, 1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, -1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 1, 3, 4, 0, 0, 0, 0, 0, 0, 1, 2, 6, 5, 0, 0, 0, 0, 0, 0, 0, 1, 4, 10, 8, 0, 0, 0, 0, 0, 0, 0, 1, 2, 7, 18, 11, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 14, 31, 18, 0, 0 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`0,26`
	LINKS	`Table of n, a(n) for n=0..90.`
	EXAMPLE	`Array starts:` `[0] 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...` `[1] 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...` `[2] 0, 1, 1, 1, 2, 2, 4, 5, 8, 11, 18, 25, 40, ...` `[3] 0, 0, 1, 1, 2, 3, 6, 10, 18, 31, 56, 96, 172, ...` `[4] 0, 0, 0, 1, 1, 2, 4, 7, 14, 26, 50, 93, 178, ...` `[5] 0, 0, 0, 0, 1, 1, 2, 4, 8, 15, 30, 58, 114, ...` `[6] 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 62, ...` `[7] 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, ...` `[8] 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, ...` `[9] 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, ...` `.` `Compare the rows with the columns of A349802.`
	MAPLE	`read transforms;` `F := proc(n, k) option remember;` `ifelse(k < 2, k, add(F(n, k-j), j = 1..min(n, k))) end:` `Frow := (n, len) -> [seq(0, j = 0..n-3), seq(F(n, k), k = 0..len)]:` `Arow := (n, len) -> EULERi(Frow(n, len)):` `for n from 0 to 9 do Arow(n, 14 - n) od;`
	CROSSREFS	`Rows are the inverse Euler transforms of A063524, A057427, A000045, A000073, A000078, A001591, A001592.` `Cf. A092921, A349802` `Sequence in context: A281245 A284499 A280457 * A308118 A017857 A127842` `Adjacent sequences: A349900 A349901 A349902 * A349904 A349905 A349906`
	KEYWORD	`sign,tabl`
	AUTHOR	`Peter Luschny, Dec 05 2021`
	STATUS	`approved`

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)