login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A272569 A variation on Stern's diatomic sequence. 1
0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 6, 1, 6, 2, 3, 0, 4, 3, 10, 2, 15, 6, 12, 1, 12, 6, 15, 2, 10, 3, 4, 0, 5, 4, 14, 3, 24, 10, 21, 2, 28, 15, 40, 6, 35, 12, 20, 1, 20, 12, 35, 6, 40, 15, 28, 2, 21, 10, 24, 3, 14, 4, 5, 0, 6, 5, 18, 4, 33, 14, 30, 3, 44, 24, 65, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
This sequence has an analogous relationship to A001654 as A002487 has to A000045; maxima between a(2^n) and a(2^n+1) = A001654(n).
For 2^k<=n<=2^k+1: a(n) = A002487(2^(k+1)-n)*A002487(n-2^k).
LINKS
Sam Northshield, Three analogues of Stern's diatomic sequence, arXiv preprint arXiv:1503.03433 [math.CO], 2015; also, Proceedings of the 16th International Conference on Fibonacci Numbers and Their Applications, Rochester Institute of Technology, Rochester, New York, July 20-27, 2014.
Sam Northshield, Some generalizations of a formula of Reznick, SUNY Plattsburgh (2022).
FORMULA
a(2n) = a(n), a(2n+1) = a(n) + a(n+1) + (4a(n)*a(n+1)+1)^(1/2).
MATHEMATICA
nn = 100;
a[_] = 0; a[1] = 0; Do[a[n] = If[EvenQ[n], a[n/2], m = (n-1)/2; a[m] + a[m + 1] + Sqrt[1 + 4 a[m] a[m+1]] // Floor], {n, 2, nn}];
Array[a, nn] (* Jean-François Alcover, Sep 25 2018, from PARI *)
PROG
(PARI) lista(nn) = {va = vector(nn); va[1] = 0; for (n=2, nn, if (n % 2 == 0, va[n] = va[n/2], m = (n-1)/2; va[n] = va[m] + va[m+1] + sqrtint(1 + 4*va[m]*va[m+1])); ); va; } \\ Michel Marcus, May 03 2016
CROSSREFS
Sequence in context: A365385 A366788 A290537 * A344788 A068076 A138498
KEYWORD
nonn
AUTHOR
Max Barrentine, May 02 2016
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)