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 A094864 #50 Aug 12 2025 01:58:39
%S A094864 1,2,6,18,53,154,443,1264,3582,10092,28291,78962,219541,608318,
%T A094864 1680438,4629414,12722033,34882954,95451407,260698732,710802606,
%U A094864 1934955072,5259642751,14277467618,38707663273,104816737274,283521290598,766112145594,2068131437357
%N A094864 a(0)=1, a(1)=2, a(2)=6, a(3)=18; for n >= 4, a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
%H A094864 Jinyuan Wang, <a href="/A094864/b094864.txt">Table of n, a(n) for n = 0..1000</a>
%H A094864 Bayo Musa Ahmed, Nadia Aldhamri, Fatma Al-Kharousi, Georg Klein, and Abdullahi Umar, <a href="https://arxiv.org/abs/2203.06417">Combinatorial results for order-preserving partial injective contraction mappings</a>, arXiv:2203.06417 [math.CO], 2022. See also <a href="https://cdm.ucalgary.ca/article/view/62669">Contrib. Disc. Math.</a> (2024) Vol. 19, No. 2, 1-19. See pp. 2, 11, 12.
%H A094864 Elena Barcucci, Renzo Pinzani, and Renzo Sprugnoli, <a href="http://dx.doi.org/10.1007/3-540-56610-4_71">Directed column-convex polyominoes by recurrence relations</a>, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
%H A094864 Manosij Ghosh Dastidar and Michael Wallner, <a href="https://arxiv.org/abs/2402.17849">Bijections and congruences involving lattice paths and integer compositions</a>, arXiv:2402.17849 [math.CO], 2024. See p. 23.
%H A094864 S. Rinaldi and D. G. Rogers, <a href="http://norcom.math.aau.dk/stacks.pdf">How the odd terms in the Fibonacci sequence stack up</a>, 8th Nordic Comb. Conf, Aalborg, Denmark, Oct 20 2004. [Broken link]
%H A094864 S. Rinaldi and D. G. Rogers, <a href="http://www.jstor.org/stable/40378191">How the odd terms in the Fibonacci sequence stack up</a>, Math. Gaz. vol 90, no 519 (2006) pp. 431-442.
%H A094864 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
%F A094864 O.g.f: -(2*x-1)*(x-1)^2/(x^2-3*x+1)^2 = (-1-2*x)/(x^2-3*x+1)+(2-5*x)/(x^2-3*x+1)^2. - _R. J. Mathar_, Dec 02 2007
%F A094864 a(n) = (2*F(2*n+3)+(n-1)*L(2*n-1))/5, where F(n) is the n-th Fibonacci number and L(n) is the n-th Lucas number. - _Rigoberto Florez_, Jul 29 2019
%t A094864 Table[((n - 1)*LucasL[2n-1] + 2*Fibonacci[2n+3])/5, {n, 0, 28}] (* _Rigoberto Florez_, Jul 29 2019 *)
%t A094864 LinearRecurrence[{6, -11, 6, -1}, {1, 2, 6, 18}, 40] (* _Vincenzo Librandi_, Jul 30 2019 *)
%o A094864 (PARI) Vec(-(2*x-1)*(x-1)^2/(x^2-3*x+1)^2 + O(x^40)) \\ _Michel Marcus_, Feb 14 2016
%o A094864 (Magma) I:=[1,2,6,18]; [n le 4 select I[n] else 6*Self(n-1)-11*Self(n-2)+6*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jul 30 2019
%K A094864 nonn,easy
%O A094864 0,2
%A A094864 _N. J. A. Sloane_, Jun 14 2004