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URL: https://oeis.org/A385107

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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.
1
1, 2, 4, 8, 15, 27, 48, 86, 157, 292, 549, 1034, 1939, 3613, 6697, 12381, 22889, 42384, 78642, 146136, 271720, 505137, 938514, 1742620, 3234360, 6002359, 11140379, 20680696, 38398206, 71302165, 132404188, 245856269, 456491098, 847539571, 1573534749, 2921413881, 5423970485, 10070489177
OFFSET
1,2
COMMENTS
a(n) is the number of subsets of {4, 8, 12,.., 4*n} that are Schreier and contain 4*n.
LINKS
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 1 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 1).
FORMULA
a(n) = 2 + Sum_{i=1..n-2} Sum_{j=0..4i-2} binomial(n-i-1,j), for n > 1.
a(n) = A103372(4*n).
G.f.: x*(1 - 2*x + 2*x^2)/(1 - 4*x + 6*x^2 - 4*x^3 + x^4 - x^5).
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1, 1}, {1, 2, 4, 8, 15}, 50] (* Paolo Xausa, Jun 25 2025 *)
CROSSREFS
Sequence in context: A074029 A248729 A138653 * A367223 A284275 A054159
KEYWORD
nonn,easy,changed
AUTHOR
Hung Viet Chu, Jun 18 2025
STATUS
approved