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2k-1 appears 2k times after 2k-2 appears once.
2

%I #22 Jul 20 2022 08:52:36

%S 0,1,1,2,3,3,3,3,4,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,

%T 9,10,11,11,11,11,11,11,11,11,11,11,11,11,12,13,13,13,13,13,13,13,13,

%U 13,13,13,13,13,13,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16

%N 2k-1 appears 2k times after 2k-2 appears once.

%H Seiichi Manyama, <a href="/A316355/b316355.txt">Table of n, a(n) for n = 0..10000</a>

%F a(k^2-1) = 2k-2.

%F G.f.: ((1+x)*Theta_3(0,x)-1-3*x)/(2*x-2*x^2) where Theta_3 is a Jacobi Theta function. - _Robert Israel_, Jul 01 2018

%p seq(op([2*k-2,(2*k-1)$(2*k)]),k=1..10); # _Robert Israel_, Jul 01 2018

%Y Cf. A005563, A316354.

%Y Essentially partial sums of A267006.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jun 30 2018