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 A322325 #25 May 06 2020 11:02:45
%S A322325 1,1,2,4,9,21,49,115,269,630,1474,3450,8073,18893,44212,103465,242125,
%T A322325 566617,1325982,3103035,7261648,16993545,39767898,93063924,217786044,
%U A322325 509657890,1192689641,2791104828,6531679192,15285285161,35770272112,83708766611,195893326791
%N A322325 Number of nondecreasing Motzkin paths of length n.
%H A322325 R. Flórez and J. L. Ramírez, <a href="https://ajc.maths.uq.edu.au/pdf/72/ajc_v72_p138.pdf">Some enumerations on non-decreasing Motzkin paths</a>, Australasian Journal of Combinatorics, 72(1) (2018), 138-154.
%H A322325 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-3,0,1)
%F A322325 a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) + a(n-5), a(0)=1, a(1)=1, a(2)=2, a(3)=4, a(4)=9.
%F A322325 G.f.: (x^3 - 2*x^2 - x + 1)/(1 - 2*x - 2*x^2 + 3*x^3 - x^5).
%e A322325 For n=6 we have 49 paths. Among the A001006(6) = 51 Motzkin paths, the following two paths are not nondecreasing Motzkin paths: UHUDDH and UUDHDH.
%t A322325 LinearRecurrence[{2, 2, -3, 0, 1}, {1, 1, 2, 4, 9}, 40] (* _Amiram Eldar_, Dec 03 2018 *)
%Y A322325 Column k=0 of A322329.
%Y A322325 Cf. A001006, A001519.
%K A322325 nonn,easy
%O A322325 0,3
%A A322325 _José Luis Ramírez Ramírez_, Dec 03 2018