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%I #5 Mar 04 2013 17:53:58
%S 1,1,1,1,2,1,1,2,2,1,1,3,3,3,1,1,3,3,3,3,1,1,3,4,4,4,3,1,1,3,4,5,5,4,
%T 3,1,1,3,4,5,5,5,4,3,1,1,3,5,6,6,6,6,5,3,1,1,3,5,6,6,7,6,6,5,3,1
%N A symmetrical triangle sequence based on Dirichlet's divisors:g(n)=n*Log[n] - n + Sqrt[n];t(n,m)=If[m == 0 || m == n, 1, 1 + Round[ -g(m) - g(n - m) + g(n)]]
%C Row sums are: {1, 2, 4, 6, 11, 14, 20, 26, 31, 42, 49,...}.
%C One possible method of relating sum form symmetrical triangles to product (factorial like) form triangles is that the sums forms are related to divisors.
%C The Dirichlet divisor approximate function for the factorial (here g(n)) gives a triangle at the exponential level that is here made into integers using the Round[] function.
%D George E. Andrews, Number Theory,Dover Publications,N.Y. 1971, pp 207-208
%F g(n)=n*Log[n] - n + Sqrt[n];
%F t(n,m)=If[m == 0 || m == n, 1, 1 + Round[ -g(m) - g(n - m) + g(n)]]
%e {1},
%e {1, 1},
%e {1, 2, 1},
%e {1, 2, 2, 1},
%e {1, 3, 3, 3, 1},
%e {1, 3, 3, 3, 3, 1},
%e {1, 3, 4, 4, 4, 3, 1},
%e {1, 3, 4, 5, 5, 4, 3, 1},
%e {1, 3, 4, 5, 5, 5, 4, 3, 1},
%e {1, 3, 5, 6, 6, 6, 6, 5, 3, 1},
%e {1, 3, 5, 6, 6, 7, 6, 6, 5, 3, 1}
%t g[n_] = n*Log[n] - n + Sqrt[n];
%t t1[n_, m_] = If[m == 0 || m == n, 1, 1 + Round[ -g[m] - g[n - m] + g[n]]];
%t Table[Table[t1[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A176346
%K nonn,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Apr 15 2010
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