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 A385142 #13 Jun 28 2025 01:00:01
%S A385142 0,0,0,1,3,6,10,15,22,35,64,129,265,529,1013,1873,3394,6126,11148,
%T A385142 20552,38303,71760,134408,250880,466361,864339,1600062,2963186,
%U A385142 5494247,10200142,18952107,35221440,65442625,121544393,225655617,418857277,777451793,1443184210,2679343966
%N A385142 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) with a(1) = a(2) = a(3) = 0, a(4) = 1, and a(5) = 3.
%C A385142 a(n) is the number of subsets of {4, 8, 12,.., 4*n} that are maximal Schreier and contain 4*n.
%H A385142 Paolo Xausa, <a href="/A385142/b385142.txt">Table of n, a(n) for n = 1..1000</a>
%H A385142 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 2 p. 2.
%H A385142 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,1).
%F A385142 a(n) = Sum_{i=1..floor((n+1)/5)} binomial(n-i-1, 4i-2).
%F A385142 a(n) = A017827(4*n-6), n > 1.
%t A385142 LinearRecurrence[{4, -6, 4, -1, 1}, {0, 0, 0, 1, 3}, 50] (* _Paolo Xausa_, Jun 27 2025 *)
%Y A385142 Cf. A017827.
%K A385142 nonn,easy
%O A385142 1,5
%A A385142 _Hung Viet Chu_, Jun 19 2025