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 A385106 #33 Jun 25 2025 09:19:04
%S A385106 1,2,4,7,12,21,38,70,129,236,429,778,1412,2567,4672,8505,15478,28158,
%T A385106 51217,93160,169465,308290,560852,1020311,1856132,3376605,6142582,
%U A385106 11174374,20328113,36980404,67273829,122382762,222635316,405011895,736786328,1340341377,2438312358,4435711166
%N A385106 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) with a(1) = 1, a(2) = 2, a(3) = 4, and a(4) = 7.
%C A385106 a(n) the number of subsets of {3, 6, 9, 12, ..., 3*n} that are Schreier and contain 3*n.
%H A385106 Hung Viet Chu and Zachary Louis Vasseur, <a href="https://arxiv.org/abs/2506.14312">Schreier sets of multiples of an integer, linear recurrence, and Pascal triangle</a>, arXiv:2506.14312 [math.CO], 2025. See Table 1 p. 2.
%H A385106 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1)
%F A385106 a(n) = 2 + Sum_{i=1..n-2} Sum_{j=0..3i-2} binomial(n-i-1,j), for n > 1.
%F A385106 a(n) = A079398(3*n).
%F A385106 G.f.: x*(1 - x + x^2)/(1 - 3*x + 3*x^2 - x^3 - x^4).
%t A385106 LinearRecurrence[{3,-3,1,1},{1, 2, 4, 7},38 ] (* or *) Rest[CoefficientList[Series[x*(1 - x + x^2)/(1 - 3*x + 3*x^2 - x^3 - x^4),{x,0,38}],x]] (* or *) a[1]=1;a[n_]:=2 + Sum[Binomial[n-i-1,j],{i,n-2} ,{j,0,3i-2} ];Array[a,38] (* _James C. McMahon_, Jun 24 2025 *)
%Y A385106 Cf. A079398, A385107.
%K A385106 nonn,easy
%O A385106 1,2
%A A385106 _Hung Viet Chu_, Jun 18 2025