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A340951
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Number of ways to write n as an ordered sum of 6 nonzero triangular numbers.
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10
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1, 0, 6, 0, 15, 6, 20, 30, 15, 66, 21, 90, 61, 90, 126, 86, 210, 90, 270, 156, 261, 320, 210, 450, 261, 516, 375, 542, 495, 570, 727, 540, 870, 650, 966, 816, 1050, 906, 1155, 1266, 1020, 1560, 1090, 1710, 1416, 1698, 1635, 1746, 2120, 1650, 2376, 1980, 2316, 2490, 2368, 2520, 2835
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OFFSET
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6,3
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LINKS
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FORMULA
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G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^6, where theta_2() is the Jacobi theta function.
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MAPLE
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b:= proc(n, k) option remember; local r, t, d; r, t, d:= $0..2;
if n=0 then `if`(k=0, 1, 0) else
while t<=n do r:= r+b(n-t, k-1); t, d:= t+d, d+1 od; r fi
end:
a:= n-> b(n, 6):
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MATHEMATICA
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nmax = 62; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^6, {x, 0, nmax}], x] // Drop[#, 6] &
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CROSSREFS
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Cf. A000217, A008440, A010054, A053603, A053604, A319816, A340949, A340950, A340952, A340953, A340954, A340955.
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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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