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 A340949 Number of ways to write n as an ordered sum of 4 nonzero triangular numbers. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..10000 FORMULA G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^4, where theta_2() is the Jacobi theta function. MAPLE 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 MATHEMATICA nmax = 75; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^4, {x, 0, nmax}], x] // Drop[#, 4] & CROSSREFS 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 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 31 2021 STATUS approved

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Last modified February 6 16:43 EST 2023. Contains 360110 sequences. (Running on oeis4.)