A244475 5th-largest term in the n-th row of Stern's diatomic triangle A002487.

1, 3, 9, 16, 27, 46, 76, 123, 207, 335, 545, 882, 1428, 2311, 3740, 6051, 9791, 15842, 25633, 41475, 67108, 108583, 175691, 284274, 459965, 744239, 1204204, 1948443, 3152647, 5101090, 8253737

Offset: 3

Author

N. J. A. Sloane, Jul 01 2014

Keywords

• nonn
• more

Links

• Jennifer Lansing, Largest Values for the Stern Sequence, Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.5.

Crossrefs

Cf. A002487, A244472, A244473, A244474, 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:
A244475 := proc(n)
    {seq(A002487(n,k),k=0..2^n-1)} ;
    sort(%) ;
    op(-5,%) ;
end proc:
for n from 3 do
    print(A244475(n)) ;
od: # R. J. Mathar, Oct 25 2014

Mathematica

s[n_, k_] := s[n, k] = Which[k == 0, 1, k == 2^n-1, n+1, EvenQ[k], s[n-1, k/2], True, s[n-1, (k-1)/2] + s[n-1, (k+1)/2]];
row[n_] := Table[s[n, k], {k, 0, 2^n-1}];
a[n_] := If[n == 3, 1, Union[row[n]][[-5]]];
Table[Print[n, " ", a[n]]; a[n], {n, 3, 23}] (* Jean-François Alcover, Mar 13 2023, after R. J. Mathar *)

Python

from itertools import product
from functools import reduce
def A244475(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)[4] # Chai Wah Wu, Jun 19 2022

Formula

Conjectured g.f.: -x^3*(x^14+ x^13+ x^12+ 2*x^11 +3*x^10 +5*x^9 +8*x^8 +x^7 +3*x^6 +3*x^5 +2*x^4 +4*x^3 +5*x^2 +2*x +1) / (x^2+x-1). - Alois P. Heinz, Jun 20 2022

Extensions

a(24)-a(25) from Alois P. Heinz, Jun 19 2022

a(26)-a(33) from Chai Wah Wu, Jun 20 2022