A340954 Number of ways to write n as an ordered sum of 9 nonzero triangular numbers.

1, 0, 9, 0, 36, 9, 84, 72, 126, 261, 162, 576, 336, 882, 873, 1092, 1845, 1386, 3061, 2160, 4167, 3957, 4860, 6948, 5580, 10287, 7812, 12777, 12276, 14634, 18363, 17136, 25056, 21282, 31266, 28899, 36075, 39654, 41202, 51348, 49383, 63270, 59391, 76059, 73611, 87319, 93582, 96966

Offset

9,3

Links

Alois P. Heinz, Table of n, a(n) for n = 9..10000

Formula

G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^9, 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) elif k<1 then 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, 9):
seq(a(n), n=9..56);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 56; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^9, {x, 0, nmax}], x] // Drop[#, 9] &

Crossrefs

Cf. A000217, A010054, A053603, A053604, A226253, A319819, A340949, A340950, A340951, A340952, A340953, A340955.

Sequence in context: A167301 A177741 A182213 * A087094 A375682 A343575

Adjacent sequences: A340951 A340952 A340953 * A340955 A340956 A340957

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved