A340950 Number of ways to write n as an ordered sum of 5 nonzero triangular numbers.

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

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: A347681 A374285 A291724 * A156550 A208477 A007392

Adjacent sequences: A340947 A340948 A340949 * A340951 A340952 A340953

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved