login

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”).

A330513
a(n) = a(n-1) + a(floor(n/4)), a(1)=a(2)=a(3) = 1.
1
1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19, 21, 24, 27, 30, 33, 37, 41, 45, 49, 54, 59, 64, 69, 75, 81, 87, 93, 100, 107, 114, 121, 129, 137, 145, 153, 162, 171, 180, 189, 199, 209, 219, 229, 240, 251, 262, 273, 285, 297, 309, 321, 334, 347
OFFSET
1,4
COMMENTS
Also the number of finite sequences b(1..r) satisfying the conditions b(1) = 1, b(i+1) >= 4 b(i) for 1 <= i < r, and b(r) <= n.
LINKS
Lukas Fleischer, Samin Riasat, Jeffrey Shallit, New Bounds on Antipowers in Binary Words, arXiv:1912.08147 [cs.FL], 2019.
MAPLE
a:= proc(n) option remember;
`if`(n<4, signum(n), a(n-1)+a(iquo(n, 4)))
end:
seq(a(n), n=1..75); # Alois P. Heinz, Dec 16 2019
MATHEMATICA
Nest[Append[#1, #1[[-1]] + #1[[Floor[#2/4] ]] ] & @@ {#, Length@ # + 1} &, {1, 1, 1}, 58] (* Michael De Vlieger, Mar 04 2020 *)
CROSSREFS
Sequence in context: A032963 A033065 A269445 * A246092 A017906 A159452
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Dec 16 2019
STATUS
approved