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 A169953 #16 Sep 08 2019 03:12:06
%S A169953 1,1,4,8,15,23,44,64,117,173,262,374,571,791,1188,1644,2355,3205,4552,
%T A169953 5980,8283,10925,14702,19338,26031,33581,44690,57566,75531,96531,
%U A169953 125738,158690,204953,258325,329394,412054,523931,649973,822434,1018332,1274909
%N A169953 Third entry in row n of triangle in A169950.
%C A169953 Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?
%H A169953 <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%F A169953 a(n) = A169948(n)-A169948(n-1) for n>2. - _Andrew Howroyd_, Jul 09 2017
%t A169953 b[n_, s_] := b[n, s] = Module[{sn, m}, m = Length[s]; sn = Append[s, n]; If[n < 1, 1, b[n - 1, s] + If[m*(m + 1)/2 == Length[Union[Flatten[Table[ sn[[i]] + sn[[j]], {i, 1, m}, {j, i + 1, m + 1}]]]], b[n - 1, sn], 0]]];
%t A169953 A196723[n_] := A196723[n] = b[n - 1, {n}] + If[n == 0, 0, A196723[n - 1]]; c[n_, s_] := c[n, s] = Module[{sn, m}, If[n < 1, 1, sn = Append[s, n]; m = Length[sn]; If[m*(m - 1)/2 == Length[Table[sn[[i]] - sn[[j]], {i, 1, m - 1}, {j, i + 1, m}] // Flatten // Union], c[n-1, sn], 0] + c[n-1, s]]];
%t A169953 A143823[n_] := A143823[n] = c[n - 1, {n}] + If[n == 0, 0, A143823[n - 1]];
%t A169953 a[n_] := A196723[n+1] - A196723[n] - A143823[n+1] + A143823[n];
%t A169953 Table[Print[n, " ", a[n]]; a[n], {n, 2, 42}] (* _Jean-François Alcover_, Sep 07 2019, after _Alois P. Heinz_ in A196723 and A143823 *)
%Y A169953 Related to thickness: A169940-A169954, A061909.
%K A169953 nonn
%O A169953 2,3
%A A169953 _N. J. A. Sloane_, Aug 01 2010
%E A169953 a(15)-a(28) and definition corrected by _Nathaniel Johnston_, Nov 15 2010
%E A169953 Offset corrected and a(30)-a(42) from _Andrew Howroyd_, Jul 09 2017