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.

0, 0, 0, 1, 3, 6, 10, 15, 22, 35, 64, 129, 265, 529, 1013, 1873, 3394, 6126, 11148, 20552, 38303, 71760, 134408, 250880, 466361, 864339, 1600062, 2963186, 5494247, 10200142, 18952107, 35221440, 65442625, 121544393, 225655617, 418857277, 777451793, 1443184210, 2679343966

Offset

1,5

Comments

a(n) is the number of subsets of {4, 8, 12,.., 4*n} that are maximal Schreier and contain 4*n.

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Hùng Việt Chu and Zachary Louis Vasseur, Schreier sets of multiples of an integer, linear recurrence, and Pascal triangle, arXiv:2506.14312 [math.CO], 2025. See Table 2 p. 2.

Hùng Việt Chu and Zachary Louis Vasseur, Linear Recurrences of Generalized Schreier Sets Revisited, J. Int. Seq. 29 (2026), Article 26.2.2. See p. 3 (Table 2).

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1).

Formula

a(n) = Sum_{i=1..floor((n+1)/5)} binomial(n-i-1, 4*i-2).

a(n) = A017827(4*n-6), n > 1.

G.f.: x^4*(1 - x)/((x - 1)^4 - x^5). - Elmo R. Oliveira, Apr 01 2026

Mathematica

LinearRecurrence[{4, -6, 4, -1, 1}, {0, 0, 0, 1, 3}, 50] (* Paolo Xausa, Jun 27 2025 *)

Crossrefs

Cf. A017827.

Sequence in context: A209231 A137358 A143963 * A139714 A373962 A342211

Adjacent sequences: A385139 A385140 A385141 * A385143 A385144 A385145

Keyword

nonn,easy

Author

Hung Viet Chu, Jun 19 2025

Status

approved