A244474 - OEIS

%I #17 Mar 12 2023 10:45:00

%S 2,4,10,17,29,47,79,128,208,337,546,883,1429,2312,3741,6053,9794,

%T 15847,25641,41488,67129,108617

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

%H Jennifer Lansing, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Lansing/lansing2.html">Largest Values for the Stern Sequence</a>, J. Integer Seqs., 17 (2014), #14.7.5.

%F 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

%p A002487 := proc(n,k)

%p     option remember;

%p     if k =0 then

%p         1;

%p     elif k = 2^n-1 then

%p         n+1 ;

%p     elif type(k,'even') then

%p         procname(n-1,k/2) ;

%p     else

%p         procname(n-1,(k-1)/2)+procname(n-1,(k+1)/2) ;

%p     end if;

%p end proc:

%p A244474 := proc(n)

%p     {seq(A002487(n,k),k=0..2^n-1)} ;

%p     sort(%) ;

%p     op(-4,%) ;

%p end proc:

%p for n from 3 do

%p     print(A244474(n)) ;

%p od: # _R. J. Mathar_, Oct 25 2014

%t 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 T = Table[s[n], {n, 0, 2^25}] // Flatten // SplitBy[#, If[# == 1, 1, 0]&]& // DeleteCases[#, {1}]&;

%t Union[#][[-4]]& /@ T[[5 ;;]] (* _Jean-François Alcover_, Mar 12 2023 *)

%o (Python)

%o from itertools import product

%o from functools import reduce

%o 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

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

%K nonn,more

%O 3,1

%A _N. J. A. Sloane_, Jul 01 2014

%E a(24) from _Jean-François Alcover_, Mar 12 2023