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%I #18 Mar 23 2023 07:57:22
%S 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,
%T 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,
%U 14,75,4,89,15,93,0,108,19,108,5,127,19,132,2,151,24,153,5,177,26,182,1
%N 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.
%H Winston de Greef, <a href="/A361734/b361734.txt">Table of n, a(n) for n = 0..10000</a>
%H Cristina Ballantine and George Beck, <a href="https://arxiv.org/abs/2303.11493">Partitions enumerated by self-similar sequences</a>, arXiv:2303.11493 [math.CO], 2023. See p. 12.
%F a(n) = 0 <=> n in { A000079 }.
%p a:= proc(n) option remember; `if`(n<2, 1-n,
%p `if`(n::even, a(n/2), a(n-2)+a(n-3)))
%p end:
%p seq(a(n), n=0..80); # _Alois P. Heinz_, Mar 22 2023
%o (PARI) a(n) = if (n <= 1, return(1-n)); if (n%2, a(n-2) + a(n-3), a(n/2));
%Y Cf. A000079, A361735, A361736.
%K nonn
%O 0,10
%A _Michel Marcus_, Mar 22 2023
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