A366064 Record values of A366091.

1, 2, 3, 4, 5, 7, 8, 11, 15, 16, 19, 21, 23, 24, 25, 28, 32, 33, 34, 39, 48, 50, 60, 64, 65, 74, 78, 79, 84, 90, 92, 96, 102, 104, 112, 113, 129, 133, 136, 137, 149, 153, 163, 165, 176, 178, 190, 192, 196, 200, 209, 226, 237, 244, 253, 273, 284, 299, 316, 317, 320, 329, 347, 360, 361, 380, 385

Offset

1,2

Comments

Numbers m such that for some v, there are exactly m ways to write v = i^2 + 2*j^2 + 3*k^2 with i,j,k >= 0, and fewer than m ways to write w = i^2 + 2*j^2 + 3*k^2 for every w < v.

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = A366091(A366065(n)).

Example

a(6) = 7 is a term because 36 = 6^2 + 2*0^2 + 3*0^2 = 2^2 + 2*4^2 + 3*0^2
= 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.

Maple

g:= add(z^(i^2), i=0..500) * add(z^(2*i^2), i=0..floor(500/sqrt(2))) *
add(z^(3*i^2), i=0..floor(500/sqrt(3))):
S:= series(g, z, 250001):
L:= [seq(coeff(S, z, i), i=0..250000)]:
B:= NULL: m:= 0:
for i from 1 to 250001 do
  if L[i] > m then
     m:= L[i]; B:=B, m
  fi
od:
B;

Crossrefs

Cf. A366065, A366091.

Sequence in context: A191168 A309879 A191166 * A238484 A241340 A326667

Adjacent sequences: A366061 A366062 A366063 * A366065 A366066 A366067

Keyword

nonn

Author

Robert Israel, Sep 28 2023

Status

approved