A330500 a(n) = a(n-1) + a(floor(n/3)), a(1) = a(2) = 1.

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, 97, 106, 115, 126, 137, 148, 161, 174, 187, 203, 219, 235, 254, 273, 292, 314, 336, 358, 384, 410, 436, 466, 496, 526, 560, 594, 628, 667, 706, 745, 789, 833, 877

Offset

1,3

Comments

Also, the number of finite sequences b(1..r) satisfying b(1) = 1 and b(i+1) >= 3*b(i) and b(r) <= n.

Links

Table of n, a(n) for n=1..59.

Example

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).

Maple

a:= proc(n) option remember;
      `if`(n<2, n, a(n-1)+a(iquo(n, 3)))
    end:
seq(a(n), n=1..75);  # Alois P. Heinz, Dec 16 2019

Mathematica

Nest[Append[#1, #1[[-1]] + #1[[Floor[#2/3] ]] ] & @@ {#, Length@ # + 1} &, {1, 1}, 57] (* Michael De Vlieger, Dec 16 2019 *)

Crossrefs

An analog of A033485.

Sequence in context: A026445 A279078 A308627 * A030151 A307360 A283455

Adjacent sequences: A330497 A330498 A330499 * A330501 A330502 A330503

Keyword

nonn

Author

Jeffrey Shallit, Dec 16 2019

Status

approved