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 A027082 #20 Jun 24 2020 14:15:08
%S A027082 1,1,1,1,1,1,1,3,2,1,1,1,3,5,6,5,1,1,1,3,5,9,14,16,11,1,1,1,3,5,9,17,
%T A027082 28,39,41,27,1,1,1,3,5,9,17,31,54,84,108,107,68,1,1,1,3,5,9,17,31,57,
%U A027082 102,169,246,299,283,175,1,1,1,3,5,9,17,31,57
%N A027082 Irregular triangular array: T(n,0) = 1 for n >= 1; T(n,1) = T(n,2) = 1 for n >= 1; T(n,k) = T(n-1,k-3) + T(n-1,k-2) + T(n-1,k-1) for 3 <= k <= 2n-1 and n >= 2; and T(n,2n) = T(n-1,2n-3) + T(n-1,2n-2) for n >= 2.
%H A027082 R. J. Mathar, <a href="/A027082/b027082.txt">Table of n, a(n) for n = 0..1000</a>, recomputing the old b-file for offset 0.
%e A027082 The first 6 rows:
%e A027082 1
%e A027082 1 .. 1 .. 1
%e A027082 1 .. 1 .. 1 .. 3 .. 2
%e A027082 1 .. 1 .. 1 .. 3 .. 5 .. 6 .. 5
%e A027082 1 .. 1 .. 1 .. 3 .. 5 .. 9 .. 14 .. 16 .. 11
%e A027082 1 .. 1 .. 1 .. 3 .. 5 .. 9 .. 17 .. 28 .. 39 .. 41 .. 27
%p A027082 A027082 := proc(n,k)
%p A027082 option remember;
%p A027082 if k < 0 or k > 2*n then
%p A027082 0;
%p A027082 elif k <=2 then
%p A027082 1;
%p A027082 elif k = 2*n then
%p A027082 procname(n-1,k-3)+procname(n-1,k-2) ;
%p A027082 else
%p A027082 procname(n-1,k-3)+procname(n-1,k-2)+procname(n-1,k-1) ;
%p A027082 end if;
%p A027082 end proc:
%p A027082 seq(seq(A027082(n,k),k=0..2*n),n=0..10) ; # _R. J. Mathar_, Jun 24 2020
%t A027082 t[n_, 0] := 1; t[n_, 1] := 1; t[n_, 2] := 1; t[n_, k_] := t[n, k] = If[k < 2 n, t[n - 1, k - 3] + t[n - 1, k - 2] + t[n - 1, k - 1], t[n - 1, 2 n - 3] + t[n - 1, 2 n - 2]]; u = Table[t[n, k], {n, 0, 10}, {k, 0, 2 n}]; v = Flatten[u] (* A027082 *)
%K A027082 nonn,tabf
%O A027082 0,8
%A A027082 _Clark Kimberling_
%E A027082 Corrected and edited by _Clark Kimberling_, Aug 06 2014
%E A027082 Offset corrected to 0 and b-file recomputed by _R. J. Mathar_, Jun 24 2020