A340955 Number of ways to write n as an ordered sum of 10 nonzero triangular numbers.

1, 0, 10, 0, 45, 10, 120, 90, 210, 370, 297, 930, 570, 1620, 1480, 2220, 3375, 2940, 6085, 4590, 8981, 8370, 11430, 15100, 13890, 23832, 19155, 31940, 30195, 38520, 46890, 46440, 66550, 59400, 86355, 81532, 104220, 114390, 122410, 153450, 149490, 193440, 188010, 235350, 238840

Offset

10,3

Links

Alois P. Heinz, Table of n, a(n) for n = 10..10000

Formula

G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^10, 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, 10):
seq(a(n), n=10..54);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 54; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^10, {x, 0, nmax}], x] // Drop[#, 10] &

Crossrefs

Cf. A000217, A010054, A053603, A053604, A226254, A319820, A340949, A340950, A340951, A340952, A340953, A340954.

Sequence in context: A302576 A214122 A084033 * A261943 A062255 A285771

Adjacent sequences: A340952 A340953 A340954 * A340956 A340957 A340958

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved