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

3,2

Links

Table of n, a(n) for n=3..33.

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

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

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 *)

Prog

(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

Crossrefs

Cf. A002487, A244472, A244473, A244474, A244476.

Sequence in context: A212566 A061942 A174440 * A212870 A306447 A257034

Adjacent sequences: A244472 A244473 A244474 * A244476 A244477 A244478

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 01 2014

Extensions

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

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

Status

approved