A387648 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k,2*n-6*k).

1, 0, 0, 1, 2, 0, 1, 12, 4, 1, 30, 60, 9, 56, 280, 225, 106, 840, 1681, 852, 2012, 7393, 8102, 6116, 24089, 48288, 39312, 69889, 206354, 268496, 264993, 715868, 1419892, 1498177, 2407662, 5980620, 8659497, 10078152, 21975496, 42559393, 52699770, 81920920, 178653105

Offset: 0

Author

Seiichi Manyama, Sep 04 2025

Keywords

• nonn
• new

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,2,4,0,-1,4,-4).

Crossrefs

Cf. A108480, A387647.

Programs

PARI

a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k, 2*n-6*k));

Formula

G.f.: (1-x^3-2*x^4)/((1-x^3-2*x^4)^2 - 8*x^7).

a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).