A354784 First differences of A000213, also twice A000073.

0, 0, 2, 2, 4, 8, 14, 26, 48, 88, 162, 298, 548, 1008, 1854, 3410, 6272, 11536, 21218, 39026, 71780, 132024, 242830, 446634, 821488, 1510952, 2779074, 5111514, 9401540, 17292128, 31805182, 58498850, 107596160, 197900192, 363995202, 669491554

Offset: 0

Author

N. J. A. Sloane, Jul 12 2022

Keywords

• nonn
• easy

Comments

Number of anti-palindromic compositions of n+1 of even length.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• George E. Andrews, Matthew Just, and Greg Simay, Anti-palindromic compositions, arXiv:2102.01613 [math.CO], 2021. Also Fib. Q., 60:2 (2022), 164-176. See Table 1.
• Index entries for linear recurrences with constant coefficients, signature (1,1,1).

Crossrefs

Cf. A000213, A000073, A135491 (essentially the same sequence).

Programs

Mathematica

LinearRecurrence[{1, 1, 1}, {0, 0, 2}, 50] (* Paolo Xausa, May 27 2024 *)

Formula

From Chai Wah Wu, Jul 12 2022: (Start)

a(n) = a(n-1) + a(n-2) + a(n-3) for n > 2.

G.f.: -2*x^2/(x^3 + x^2 + x - 1). (End)