A330513 - OEIS

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

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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)))

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