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A366064 Record values of A366091. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A191168 A309879 A191166 * A238484 A241340 A326667
KEYWORD
nonn
AUTHOR
Robert Israel, Sep 28 2023
STATUS
approved

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Last modified April 12 09:56 EDT 2024. Contains 371627 sequences. (Running on oeis4.)