A244474 4th-largest term in n-th row of Stern's diatomic triangle A002487.

2, 4, 10, 17, 29, 47, 79, 128, 208, 337, 546, 883, 1429, 2312, 3741, 6053, 9794, 15847, 25641, 41488, 67129, 108617

Offset: 3

Author

N. J. A. Sloane, Jul 01 2014

Keywords

• nonn
• more

Links

• Jennifer Lansing, Largest Values for the Stern Sequence, J. Integer Seqs., 17 (2014), #14.7.5.

Crossrefs

Cf. A002487, A244472, A244473, A244475, A244476.

Programs

Maple

A002487 := proc(n,k)
    option remember;
    if k =0 then
        1;
    elif k = 2^n-1 then
        n+1 ;
    elif type(k,'even') then
        procname(n-1,k/2) ;
    else
        procname(n-1,(k-1)/2)+procname(n-1,(k+1)/2) ;
    end if;
end proc:
A244474 := proc(n)
    {seq(A002487(n,k),k=0..2^n-1)} ;
    sort(%) ;
    op(-4,%) ;
end proc:
for n from 3 do
    print(A244474(n)) ;
od: # R. J. Mathar, Oct 25 2014

Mathematica

s[n_] := s[n] = Switch[n, 0, 0, 1, 1, _, If[EvenQ[n], s[n/2], s[(n - 1)/2] + s[(n - 1)/2 + 1]]];
T = Table[s[n], {n, 0, 2^25}] // Flatten // SplitBy[#, If[# == 1, 1, 0]&]& // DeleteCases[#, {1}]&;
Union[#][[-4]]& /@ T[[5 ;;]] (* Jean-François Alcover, Mar 12 2023 *)

Python

from itertools import product
from functools import reduce
def A244474(n): return sorted(set(sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if y else (x[0]+x[1],x[1]),k,(1,0))) for k in product((False,True),repeat=n)),reverse=True)[3] # Chai Wah Wu, Jun 20 2022

Formula

G.f.: (-2-2*x-4*x^2-3*x^3-2*x^4-x^5-3*x^6-2*x^7-x^8-x^9-x^10)/(-1+x+x^2) (conjectured) - Jean-François Alcover, Mar 12 2023

Extensions

a(24) from Jean-François Alcover, Mar 12 2023