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 A168259 #19 Nov 19 2022 14:51:34
%S A168259 1,2,6,14,38,96,254,656,1724,4492,11776,30774,80608,210892,552226,
%T A168259 1445374,3784308,9906482,25936206,67899344,177764618,465387226,
%U A168259 1218404344,3189806746,8351034954,21863248282,57238759726,149852900454,392320072078,1027106974446,2689001192594,7039895709776
%N A168259 Eigensequence of triangle A168258.
%C A168259 Eigensequence of triangle A168258, derived from the following operation: Shift down triangle A168258, so that rows begin [1; 1; 1,1; 2,2,1; ...] = triangle M. Then take lim_{n->oo} M^n, resulting in a left-shifted vector. Delete the first 1, getting (1, 2, 6, 14, 38, 96, ...) = this sequence.
%C A168259 a(n)/a(n-1) apparently tends to phi^2=A104457. a(19)/a(18) = 2.618104...
%H A168259 Paul Barry, <a href="http://arxiv.org/abs/1107.5490">Invariant number triangles, eigentriangles and Somos-4 sequences</a>, arXiv preprint arXiv:1107.5490 [math.CO], 2011.
%o A168259 (PARI) T(n, k) = if(binomial(k, n-k)>0, 1, 0); \\ A101688
%o A168259 mat(nn) = my(ma=matrix(nn+1, nn, n, k, T(n-1, k-1)), mb=matrix(nn, nn, n, k, n>=k)); ma*mb; \\ A168258
%o A168259 shiftm(m, nn) = my(shm=matrix(nn+1, nn+1)); shm[1,1]=1; for (n=1, nn, for(k=1, nn, shm[n+1,k] = m[n,k];);); shm;
%o A168259 lista(nn) = my(m=mat(nn), shm=shiftm(m, nn), shmnn=shm^nn); vector(nn, k, shmnn[k+1, 1]); \\ _Michel Marcus_, Nov 19 2022
%Y A168259 Cf. A104457, A168258, A168260.
%K A168259 eigen,nonn
%O A168259 1,2
%A A168259 _Gary W. Adamson_, Nov 21 2009
%E A168259 Edited and more terms from _Michel Marcus_, Nov 19 2022