A330513 a(n) = a(n-1) + a(floor(n/4)), a(1)=a(2)=a(3) = 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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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

Cf. A033485, A330500.

Sequence in context: A032963 A033065 A269445 * A246092 A017906 A159452

Adjacent sequences: A330510 A330511 A330512 * A330514 A330515 A330516

Keyword

nonn

Author

Jeffrey Shallit, Dec 16 2019

Status

approved