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 A340950 Number of ways to write n as an ordered sum of 5 nonzero triangular numbers. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 5..10000 FORMULA G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^5, 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, 5): seq(a(n), n=5..67); # Alois P. Heinz, Jan 31 2021 MATHEMATICA nmax = 67; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^5, {x, 0, nmax}], x] // Drop[#, 5] & CROSSREFS 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 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 31 2021 STATUS approved

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Last modified March 31 21:40 EDT 2023. Contains 361673 sequences. (Running on oeis4.)