login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298403 a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3. 3
1, 2, 3, 7, 15, 30, 60, 112, 209, 373, 664, 1149, 1985, 3366, 5695, 9517, 15877, 26268, 43392, 71280, 116956, 191184, 312237, 508667, 828135, 1346018, 2186735, 3548701, 5757079, 9333118, 15127052, 24506542, 39695843, 64280511, 104080748, 168491921, 272746723 (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] = 2*a[n - 1] - a[n - 3] + a[Floor[n/2]];

Table[a[n], {n, 0, 90}]  (* A298403 *)

CROSSREFS

Cf. A001622, A000045, A298338, A298402.

Sequence in context: A074742 A020873 A049958 * A177487 A153010 A076993

Adjacent sequences:  A298400 A298401 A298402 * A298404 A298405 A298406

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 10 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 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)