OFFSET
1,5
COMMENTS
Related to "Liouville's Last Theorem".
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
George E. Andrews, Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130. See L_4(n).
E. T. Bell, The form wx+xy+yz+zu, Bull. Amer. Math. Soc., 42 (1936), 377-380.
FORMULA
a(n) = sigma_2(n) - n*sigma_0(n) - A055507(n-1).
EXAMPLE
G.f.: x^4 + 2 x^5 + 6 x^6 + 8 x^7 + 16 x^8 + 20 x^9 + 32 x^10 + ...
MAPLE
with(numtheory);
D00:=n->add(tau(j)*tau(n-j), j=1..n-1);
L4:=n->sigma[2](n)-n*sigma[0](n)-D00(n);
[seq(L4(n), n=1..60)];
MATHEMATICA
a[ n_] := Length @ FindInstance[{x1 > 0, x2 > 0, x3 > 0, x4 > 0, x5 > 0, n == x1 x2 + x2 x3 + x3 x4 + x4 x5}, {x1, x2, x3, x4, x5}, Integers, 10^9]; (* Michael Somos, Nov 12 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 17 2011
STATUS
approved