A340953 Number of ways to write n as an ordered sum of 8 nonzero triangular numbers.

1, 0, 8, 0, 28, 8, 56, 56, 70, 176, 84, 336, 196, 448, 492, 504, 953, 616, 1456, 960, 1814, 1792, 1904, 3032, 2100, 4144, 3052, 4768, 4670, 5264, 6720, 5936, 8876, 7112, 10620, 9648, 11718, 12720, 13216, 15960, 15261, 19608, 17164, 23296, 21226, 25424, 26796, 27272, 32844

Offset

8,3

Links

Alois P. Heinz, Table of n, a(n) for n = 8..10000

Formula

G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^8, 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, 8):
seq(a(n), n=8..56);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 56; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^8, {x, 0, nmax}], x] // Drop[#, 8] &

Crossrefs

Cf. A000217, A007331, A010054, A053603, A053604, A319818, A340949, A340950, A340951, A340952, A340954, A340955.

Sequence in context: A011997 A187162 A197618 * A047771 A298099 A137528

Adjacent sequences: A340950 A340951 A340952 * A340954 A340955 A340956

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved