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

3,1

Links

Table of n, a(n) for n=3..24.

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

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A077635 A125754 A097870 * A301739 A152231 A285939

Adjacent sequences: A244471 A244472 A244473 * A244475 A244476 A244477

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 01 2014

Extensions

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

Status

approved