OFFSET
0,7
COMMENTS
Number of compositions (ordered partitions) of n into triangular numbers > 1.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: 1/(1 - Sum_{k>=2} x^(k*(k+1)/2)).
MAPLE
a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
add(a(n-j*(j+1)/2), j=2..isqrt(2*n))))
end:
seq(a(n), n=0..80); # Alois P. Heinz, May 02 2018
MATHEMATICA
nmax = 62; CoefficientList[Series[1/(2 + x - EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8))), {x, 0, nmax}], x]
nmax = 62; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1)/2), {k, 2, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[SquaresR[1, 8 k + 1] a[n - k], {k, 2, n}]/2; Table[a[n], {n, 0, 62}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 02 2018
STATUS
approved