%I #11 Sep 29 2023 02:45:55

%S 0,3,9,12,30,36,81,84,156,228,246,324,396,444,516,534,606,774,804,876,

%T 1164,1614,1884,2046,2244,2676,3564,3684,3756,4134,4404,4764,5124,

%U 5646,6636,6654,6924,7716,8166,8724,9804,10686,11334,12324,12846,13476,15654,17004,17796,18804,20406,20694,21036

%N Positions of records in A366091.

%C Numbers that can be written in the form i^2 + 2*j^2 + 3*k^2 with i,j,k >= 0 in more ways than any previous number.

%F A366091(a(n)) = A366064(n).

%e a(6) = 36 is a term because 36 = 6^2 + 2*0^2 + 3*0^2 = 2^2 + 2*4^2 + 3*0^2

%e = 5^2 + 2*2^2 + 3*1^2 = 1^2 + 2*4^2 + 3*1^2 = 4^2 + 2*2^2 + 3*2^2 = 3^2 + 2*0^2 + 3*3^2 = 1^2 + 2*2^2 + 3*3^2 can be written as i^2 + 2*j^2 + 3*k^2 in 7 ways, and all numbers < 36 can be written in fewer than 7 ways.

%p g:= add(z^(i^2),i=0..500) * add(z^(2*i^2),i=0..floor(500/sqrt(2))) *

%p add(z^(3*i^2),i=0..floor(500/sqrt(3))):

%p S:= series(g,z,250001):

%p L:= [seq(coeff(S,z,i),i=0..250000)]:

%p A:= NULL: m:= 0:

%p for i from 1 to 250001 do

%p if L[i] > m then

%p m:= L[i]; A:=A,i-1

%p fi

%p od:

%p A;

%Y Cf. A366064, A366091.

%K nonn

%O 1,2

%A _Robert Israel_, Sep 28 2023