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A354784
First differences of A000213, also twice A000073.
1
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
0,3
COMMENTS
Number of anti-palindromic compositions of n+1 of even length.
LINKS
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.
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)
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {0, 0, 2}, 50] (* Paolo Xausa, May 27 2024 *)
CROSSREFS
Cf. A000213, A000073, A135491 (essentially the same sequence).
Sequence in context: A000018 A357307 A306604 * A075126 A300998 A098788
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 12 2022
STATUS
approved