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A347805
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Expansion of (theta_3(x) - 1)^2 / (2 * (3 - theta_3(x))).
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7
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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
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OFFSET
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2,4
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COMMENTS
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Number of compositions (ordered partitions) of n into two or more squares.
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LINKS
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FORMULA
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a(n) = Sum_{k=2..n} A337165(n,k). (End)
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MAPLE
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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):
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MATHEMATICA
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nmax = 48; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^2/(2 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 2] &
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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