A340952 Number of ways to write n as an ordered sum of 7 nonzero triangular numbers.

1, 0, 7, 0, 21, 7, 35, 42, 35, 112, 42, 182, 112, 210, 260, 217, 462, 252, 651, 399, 728, 777, 672, 1232, 749, 1533, 1127, 1659, 1617, 1792, 2289, 1890, 2926, 2212, 3339, 2990, 3584, 3654, 4046, 4613, 4263, 5754, 4487, 6636, 5733, 6825, 7014, 7203, 8617, 7560, 10087, 8302

Offset

7,3

Links

Alois P. Heinz, Table of n, a(n) for n = 7..10000

Formula

G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^7, 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, 7):
seq(a(n), n=7..58);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 58; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^7, {x, 0, nmax}], x] // Drop[#, 7] &

Crossrefs

Cf. A000217, A010054, A053603, A053604, A226252, A319817, A340949, A340950, A340951, A340953, A340954, A340955.

Sequence in context: A052440 A246919 A167299 * A282071 A064854 A199917

Adjacent sequences: A340949 A340950 A340951 * A340953 A340954 A340955

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved