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A340950
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Number of ways to write n as an ordered sum of 5 nonzero triangular numbers.
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10
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1, 0, 5, 0, 10, 5, 10, 20, 5, 35, 11, 40, 30, 35, 55, 30, 90, 25, 100, 60, 80, 120, 60, 140, 90, 161, 100, 165, 135, 165, 210, 140, 220, 180, 265, 170, 295, 200, 285, 330, 205, 365, 260, 395, 295, 391, 350, 355, 480, 340, 455, 490, 415, 480, 515, 445, 600, 510, 565, 550, 680, 545, 555
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OFFSET
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5,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 5..10000
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FORMULA
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G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^5, 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, 5):
seq(a(n), n=5..67); # Alois P. Heinz, Jan 31 2021
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MATHEMATICA
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nmax = 67; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^5, {x, 0, nmax}], x] // Drop[#, 5] &
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CROSSREFS
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Cf. A000217, A008439, A010054, A053603, A053604, A319815, A340949, A340951, A340952, A340953, A340954, A340955.
Sequence in context: A010481 A347681 A291724 * A156550 A208477 A007392
Adjacent sequences: A340947 A340948 A340949 * A340951 A340952 A340953
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jan 31 2021
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STATUS
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approved
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