A298352 a(n) = a(n-1) + a(n-2) + a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 3, 5, 9, 15, 27, 45, 77, 127, 213, 349, 577, 941, 1545, 2513, 4103, 6661, 10841, 17579, 28547, 46253, 75013, 121479, 196841, 318669, 516087, 835333, 1352361, 2188635, 3542541, 5732721, 9277775, 15013009, 24294887, 39311999, 63613547, 102932207

Offset

0,4

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..1000

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[(n-1)/2]];
Table[a[n], {n, 0, 30}]  (* A298352 *)

Crossrefs

Cf. A001622, A000045, A298338.

Sequence in context: A291153 A147087 A140190 * A083658 A018436 A018298

Adjacent sequences: A298349 A298350 A298351 * A298353 A298354 A298355

Keyword

nonn,easy

Author

Clark Kimberling, Feb 10 2018

Status

approved