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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.

A049641 a(n) = Sum_{i=0..n} ((-1)^i)*T(i,n-i), array T as in A049639.

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%I A049641 #12 Dec 08 2017 23:33:30
%S A049641 0,0,2,0,3,0,5,0,7,0,11,0,13,0,19,0,23,0,29,0,33,0,43,0,47,0,59,0,65,
%T A049641 0,73,0,81,0,97,0,103,0,121,0,129,0,141,0,151,0,173,0,181,0,201,0,213,
%U A049641 0,231,0,243,0,271,0,279,0,309,0,325,0,345,0,361,0,385
%N A049641 a(n) = Sum_{i=0..n} ((-1)^i)*T(i,n-i), array T as in A049639.
%H A049641 G. C. Greubel, <a href="/A049641/b049641.txt">Table of n, a(n) for n = 0..75</a>
%t A049641 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[(-1)^k*a[k, n - k], {k, 0, n}], {n, 0, 25}] (* _G. C. Greubel_, Dec 07 2017 *)
%Y A049641 Cf. A005728, A049643.
%K A049641 nonn
%O A049641 0,3
%A A049641 _Clark Kimberling_
%E A049641 Terms a(42) onward added by _G. C. Greubel_, Dec 07 2017