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A298339 a(n) = a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3. 3
1, 2, 3, 7, 13, 23, 43, 73, 129, 215, 367, 605, 1015, 1663, 2751, 4487, 7367, 11983, 19565, 31763, 51695, 83825, 136125, 220555, 357695, 579265, 938623, 1519551, 2460925, 3983227, 6448639, 10436353, 16892359, 27336079, 44240421, 71588483, 115848469 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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] = 2; a[2] = 3;

a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/2]];

Table[a[n], {n, 0, 30}]  (* A298339 *)

CROSSREFS

Cf. A001622, A000045, A298338.

Sequence in context: A144104 A088175 A271827 * A091440 A175211 A330028

Adjacent sequences:  A298336 A298337 A298338 * A298340 A298341 A298342

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 09 2018

STATUS

approved

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Last modified January 17 09:32 EST 2020. Contains 330949 sequences. (Running on oeis4.)