

A330500


a(n) = a(n1) + a(floor(n/3)), a(1) = a(2) = 1.


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
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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(n1)+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



