A340949 Number of ways to write n as an ordered sum of 4 nonzero triangular numbers.

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

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 A374970

Adjacent sequences: A340946 A340947 A340948 * A340950 A340951 A340952

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved