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%I #12 Jul 06 2024 11:54:31
%S 1,3,8,15,27,43,65,94,130,175,229,294,369,456,557,671,800,944,1105,
%T 1283,1479,1695,1930,2187,2465,2765,3090,3439,3813,4213,4641,5096,
%U 5580,6095,6639,7216,7825,8466,9143,9855
%N a(n) = max_{r=1..n-1} ceiling(t(t(n)-t(r-1))/(n-r+1)), where t() = triangular numbers A000217.
%C Another lower bound for Honaker triangle problem (A047837); conjectured to be exact value.
%F Empirical g.f.: -x*(x^15 - 3*x^14 + 3*x^13 - 5*x^12 + 5*x^11 - 9*x^10 + 7*x^9 - 10*x^8 + 7*x^7 - 9*x^6 + 5*x^5 - 6*x^4 + 2*x^3 - 3*x^2 - 1) / ((x-1)^4*(x^2-x+1)*(x^2+1)*(x^2+x+1)^2*(x^4-x^2+1)). [_Colin Barker_, Jan 18 2013]
%Y Cf. A047837, A047866.
%K easy,nonn
%O 1,2
%A _Mike Keith_