A057744 Expansion of (1-2*x^3)/(1-2*x-x^3+2*x^4).

1, 2, 4, 7, 14, 28, 55, 110, 220, 439, 878, 1756, 3511, 7022, 14044, 28087, 56174, 112348, 224695, 449390, 898780, 1797559, 3595118, 7190236, 14380471, 28760942, 57521884, 115043767, 230087534, 460175068, 920350135, 1840700270, 3681400540

Offset: 0

Author

N. J. A. Sloane, Oct 30 2000

Keywords

• nonn
• easy

Links

• Kevin Ryde, Iterations of the Dragon Curve, see index "JN".
• Index entries for linear recurrences with constant coefficients, signature (2,0,1,-2).

Crossrefs

Cf. A033129, A294627 (first differences).

Programs

Mathematica

LinearRecurrence[{2, 0, 1, -2}, {1, 2, 4, 7}, 30] (* Jinyuan Wang, Apr 07 2020 *)

PARI

Vec((1-2*x^3)/(1-2*x-x^3+2*x^4) + O(x^50)) \\ Michel Marcus, Dec 09 2014

Formula

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

a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 7, a(n) = 2*a(n-1) + a(n-3) - 2*a(n-4) for n > 3. - Jinyuan Wang, Apr 08 2020

a(n) = ceiling((6/7)*2^n) = (6*2^n + 2^(n mod 3))/7. - Kevin Ryde, Aug 25 2021