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A347805 Expansion of (theta_3(x) - 1)^2 / (2 * (3 - theta_3(x))). 7
1, 1, 1, 3, 4, 5, 7, 10, 16, 22, 30, 43, 62, 88, 123, 175, 249, 354, 502, 710, 1006, 1427, 2024, 2869, 4068, 5767, 8176, 11593, 16436, 23301, 33033, 46832, 66398, 94137, 133461, 189211, 268252, 380315, 539192, 764433, 1083764, 1536498, 2178364, 3088365, 4378502, 6207581, 8800750 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,4
COMMENTS
Number of compositions (ordered partitions) of n into two or more squares.
LINKS
FORMULA
From Alois P. Heinz, Sep 14 2021: (Start)
a(n) = A006456(n) - A010052(n).
a(n) = Sum_{k=2..n} A337165(n,k). (End)
MAPLE
b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0), add((
s->`if`(s>n, 0, b(n-s, max(0, t-1))))(j^2), j=1..isqrt(n)))
end:
a:= n-> b(n, 2):
seq(a(n), n=2..48); # Alois P. Heinz, Sep 14 2021
MATHEMATICA
nmax = 48; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^2/(2 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 2] &
CROSSREFS
Sequence in context: A162311 A003312 A022440 * A088130 A046840 A057773
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 14 2021
STATUS
approved

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Last modified June 23 11:51 EDT 2024. Contains 373647 sequences. (Running on oeis4.)