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 A356619 #23 Sep 04 2022 12:55:57
%S A356619 0,1,4,11,25,52,103,198,374,699,1298,2401,4431,8166,15037,27676,50924,
%T A356619 93685,172336,316999,583077,1072472,1972611,3628226,6673378,12274287,
%U A356619 22575966,41523709,76374043,140473802,258371641,475219576,874065112,1607656425
%N A356619 a(n) = number of k-tuples (u(1), u(2), ..., u(k)) with 1 <= u(1) < u(2) < ... < u(k) <= n such that u(i) - u(i-1) <= 3 for i = 2,...,k.
%H A356619 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,-1,1).
%F A356619 G.f.: x*(1 + x + x^2)/((-1 + x)^2*(1 - x - x^2 - x^3)).
%F A356619 a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5).
%F A356619 a(n) = A221949(n+2)-1 for n >= 0.
%t A356619 maxDiff = 3;
%t A356619 t = Map[Length[Select[Map[{#, Max[Differences[#]]} &,
%t A356619 Drop[Subsets[Range[#]], # + 1]], #[[2]] <= maxDiff &]] &, Range[16]]
%t A356619 FindGeneratingFunction[%, x]
%t A356619 FindLinearRecurrence[t]
%t A356619 LinearRecurrence[{3, -2, 0, -1, 1}, {0, 1, 4, 11, 25}, 45]
%Y A356619 Cf. A001891, A062544, A221949, A356620, A356621.
%K A356619 nonn,easy
%O A356619 0,3
%A A356619 _Clark Kimberling_, Aug 24 2022