A298340 a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 3, 5, 9, 15, 25, 41, 69, 113, 185, 303, 493, 801, 1303, 2113, 3425, 5553, 8993, 14561, 23579, 38165, 61769, 99975, 161785, 261801, 423655, 685525, 1109249, 1794887, 2904249, 4699249, 7603683, 12303117, 19906985, 32210405, 52117693, 84328401

Offset: 0

Author

Clark Kimberling, Feb 09 2018

Keywords

• nonn
• easy

Comments

a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..999

Crossrefs

Cf. A001622, A000045, A298338.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]];
Table[a[n], {n, 0, 30}]  (* A298340 *)