Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Dec 16 2019 20:05:20
%S 1,1,2,3,4,5,6,7,9,11,13,16,19,22,26,30,34,39,44,49,55,61,67,74,81,88,
%T 97,106,115,126,137,148,161,174,187,203,219,235,254,273,292,314,336,
%U 358,384,410,436,466,496,526,560,594,628,667,706,745,789,833,877
%N a(n) = a(n-1) + a(floor(n/3)), a(1) = a(2) = 1.
%C Also, the number of finite sequences b(1..r) satisfying b(1) = 1 and b(i+1) >= 3*b(i) and b(r) <= n.
%e For n = 10 the 11 sequences enumerated are (1), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9), (1,10), (1,3,9), (1,3,10).
%p a:= proc(n) option remember;
%p `if`(n<2, n, a(n-1)+a(iquo(n, 3)))
%p end:
%p seq(a(n), n=1..75); # _Alois P. Heinz_, Dec 16 2019
%t Nest[Append[#1, #1[[-1]] + #1[[Floor[#2/3] ]] ] & @@ {#, Length@ # + 1} &, {1, 1}, 57] (* _Michael De Vlieger_, Dec 16 2019 *)
%Y An analog of A033485.
%K nonn
%O 1,3
%A _Jeffrey Shallit_, Dec 16 2019