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

Offset: 0

Author

Peter Luschny, Dec 05 2021

Keywords

• sign
• tabl

Examples

			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.
		

Crossrefs

Rows are the inverse Euler transforms of A063524, A057427, A000045, A000073, A000078, A001591, A001592.

Cf. A092921, A349802

Programs

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;