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 A213487 #11 Jun 19 2024 17:53:25
%S A213487 1,5,15,37,77,138,223,338,489,679,911,1191,1525,1916,2367,2884,3473,
%T A213487 4137,4879,5705,6621,7630,8735,9942,11257,12683,14223,15883,17669,
%U A213487 19584,21631,23816,26145,28621,31247,34029,36973,40082,43359,46810
%N A213487 Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y|+|y-w| <= w+x+y.
%C A213487 For a guide to related sequences, see A212959.
%H A213487 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-7,4,-1).
%F A213487 a(n) = 4*a(n-1)-7*a(n-2)+8*a(n-3)-7*a(n-4)+4*a(n-5)-a(n-6).
%F A213487 G.f.: (1 + x + 2*x^2 + 4*x^3 + x^4)/((1 - x)^4 (1 + x^2)).
%F A213487 a(n) = (n+1)^3 - A213486(n).
%t A213487 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w + x + y >= Abs[w - x] + Abs[x - y] + Abs[y - w], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213487 m = Map[t[#] &, Range[0, 60]] (* A213487 *)
%t A213487 LinearRecurrence[{4,-7,8,-7,4,-1},{1,5,15,37,77,138},50] (* _Harvey P. Dale_, Jun 19 2024 *)
%Y A213487 Cf. A212959, A213486.
%K A213487 nonn,easy
%O A213487 0,2
%A A213487 _Clark Kimberling_, Jun 13 2012