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A244474 4th-largest term in n-th row of Stern's diatomic triangle A002487. 4
2, 4, 10, 17, 29, 47, 79, 128, 208, 337, 546, 883, 1429, 2312, 3741, 6053, 9794, 15847, 25641, 41488, 67129, 108617 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
LINKS
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
Sequence in context: A077635 A125754 A097870 * A301739 A152231 A285939
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Jul 01 2014
EXTENSIONS
a(24) from Jean-François Alcover, Mar 12 2023
STATUS
approved

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Last modified July 13 06:34 EDT 2024. Contains 374267 sequences. (Running on oeis4.)