This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049640 #10 Dec 16 2017 05:27:07
%S A049640 0,0,2,4,7,10,15,20,27,34,45,56,69,82,101,120,143,166,195,224,257,290,
%T A049640 333,376,423,470,529,588,653,718,791,864,945,1026,1123,1220,1323,1426,
%U A049640 1547,1668,1797,1926,2067,2208,2359,2510,2683,2856,3037,3218,3419,3620,3833,4046,4277,4508
%N A049640 a(n) = Sum_{i=0..n} T(i,n-i), array T as in A049639.
%H A049640 G. C. Greubel, <a href="/A049640/b049640.txt">Table of n, a(n) for n = 0..75</a>
%t A049640 a[0 | 1, 0 | 1] = 0; a[0 | 1, _] = a[_, 0 | 1] = 1; a[i_, j_] := Module[{slopes, cnt}, slopes = Union@Flatten@Table[(k - j)/(h - i), {h, 0, i - 1}, {k, 0, j - 1}]; cnt[slope_] := Count[Flatten[Table[{h, k}, {h, 0, i - 1}, {k, 0, j - 1}], 1], {h_, k_} /; (k - j)/(h - i) == slope]; Count[cnt /@ slopes, c_ /; c >= 2] + 2]; Table[Sum[a[k, n - k], {k, 0, n}], {n, 0, 25}] (* _G. C. Greubel_, Dec 15 2017 *)
%K A049640 nonn
%O A049640 0,3
%A A049640 _Clark Kimberling_
%E A049640 Terms a(41) and beyond added by _G. C. Greubel_, Dec 15 2017