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A340949
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Number of ways to write n as an ordered sum of 4 nonzero triangular numbers.
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10
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1, 0, 4, 0, 6, 4, 4, 12, 1, 16, 6, 16, 12, 12, 22, 8, 36, 4, 30, 24, 21, 36, 18, 36, 28, 48, 16, 44, 36, 44, 48, 36, 46, 40, 72, 20, 73, 48, 54, 72, 42, 68, 56, 84, 50, 72, 78, 56, 84, 84, 62, 112, 60, 60, 110, 84, 97, 72, 120, 76, 116, 84, 72, 144, 102, 104, 96, 108, 102, 156, 102, 92
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OFFSET
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4,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 4..10000
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FORMULA
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G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^4, 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, 4):
seq(a(n), n=4..75); # Alois P. Heinz, Jan 31 2021
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MATHEMATICA
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nmax = 75; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^4, {x, 0, nmax}], x] // Drop[#, 4] &
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CROSSREFS
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Cf. A000217, A008438, A010054, A053603, A053604, A319814, A340950, A340951, A340952, A340953, A340954, A340955.
Sequence in context: A305731 A279433 A096272 * A021715 A327278 A278210
Adjacent sequences: A340946 A340947 A340948 * A340950 A340951 A340952
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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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