login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298340 a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 1, a(2) = 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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..999

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 *)

CROSSREFS

Cf. A001622, A000045, A298338.

Sequence in context: A128587 A001595 A092369 * A061969 A034084 A018342

Adjacent sequences:  A298337 A298338 A298339 * A298341 A298342 A298343

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 09 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)