A361734 Semi-Padovan sequence: a(2*n) = a(n) and a(2*n+1) = a(2*n-1) + a(2*n-2), with a(0) = 1 and a(1) = 0.

1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 3, 1, 4, 0, 5, 2, 5, 1, 7, 2, 8, 1, 10, 3, 11, 1, 14, 4, 15, 0, 19, 5, 19, 2, 24, 5, 26, 1, 31, 7, 32, 2, 39, 8, 41, 1, 49, 10, 50, 3, 60, 11, 63, 1, 74, 14, 75, 4, 89, 15, 93, 0, 108, 19, 108, 5, 127, 19, 132, 2, 151, 24, 153, 5, 177, 26, 182, 1

Offset

0,10

Links

Winston de Greef, Table of n, a(n) for n = 0..10000

Cristina Ballantine and George Beck, Partitions enumerated by self-similar sequences, arXiv:2303.11493 [math.CO], 2023. See p. 12.

Formula

a(n) = 0 <=> n in { A000079 }.

Maple

a:= proc(n) option remember; `if`(n<2, 1-n,
      `if`(n::even, a(n/2), a(n-2)+a(n-3)))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Mar 22 2023

Prog

(PARI) a(n) = if (n <= 1, return(1-n)); if (n%2, a(n-2) + a(n-3), a(n/2));

Crossrefs

Cf. A000079, A361735, A361736.

Sequence in context: A202327 A243546 A243554 * A263111 A260438 A112197

Adjacent sequences: A361731 A361732 A361733 * A361735 A361736 A361737

Keyword

nonn

Author

Michel Marcus, Mar 22 2023

Status

approved