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 A385107 #31 Jun 25 2025 09:14:36
%S A385107 1,2,4,8,15,27,48,86,157,292,549,1034,1939,3613,6697,12381,22889,
%T A385107 42384,78642,146136,271720,505137,938514,1742620,3234360,6002359,
%U A385107 11140379,20680696,38398206,71302165,132404188,245856269,456491098,847539571,1573534749,2921413881,5423970485,10070489177
%N A385107 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) with a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 8, and a(5) = 15.
%C A385107 a(n) is the number of subsets of {4, 8, 12,.., 4*n} that are Schreier and contain 4*n.
%H A385107 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 A385107 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,1).
%F A385107 a(n) = 2 + Sum_{i=1..n-2} Sum_{j=0..4i-2} binomial(n-i-1,j), for n > 1.
%F A385107 a(n) = A103372(4*n).
%F A385107 G.f.: x*(1 - 2*x + 2*x^2)/(1 - 4*x + 6*x^2 - 4*x^3 + x^4 - x^5).
%t A385107 LinearRecurrence[{4, -6, 4, -1, 1}, {1, 2, 4, 8, 15}, 50] (* _Paolo Xausa_, Jun 25 2025 *)
%Y A385107 Cf. A103372, A385106.
%K A385107 nonn,easy
%O A385107 1,2
%A A385107 _Hung Viet Chu_, Jun 18 2025