A016029 a(1) = a(2) = 1, a(2n + 1) = 2*a(2n) and a(2n) = 2*a(2n - 1) + (-1)^n.

1, 1, 2, 5, 10, 19, 38, 77, 154, 307, 614, 1229, 2458, 4915, 9830, 19661, 39322, 78643, 157286, 314573, 629146, 1258291, 2516582, 5033165, 10066330, 20132659, 40265318, 80530637, 161061274, 322122547, 644245094

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

Row sums of Riordan array ((1+x^3)/(1-x^4), x/(1-x)). - Paul Barry, Oct 08 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,2).

Programs

Magma

[Round(3*2^(n-1)/5): n in [1..41]]; // G. C. Greubel, Jul 08 2022

Mathematica

LinearRecurrence[{2,-1,2}, {1,1,2}, 31] (* Ray Chandler, Sep 23 2015 *)

SageMath

[(1/10)*(3*2^n + 2*i^n*(((n+1)%2) - 2*i*(n%2))) for n in (1..40)] # G. C. Greubel, Jul 08 2022

Formula

From Ralf Stephan, Jan 12 2005: (Start)

a(n) = (1/10)*(3*2^n + 3*(-1)^floor(n/2) - (-1)^floor((n+1)/2)).

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

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3). - Paul Curtz, Dec 18 2007

From G. C. Greubel, Jul 08 2022: (Start)

a(n) = round( 3*2^(n-1)/5 ).

E.g.f.: (1/10)*(3*exp(2*x) + 4*sin(x) + 2*cos(x) - 5). (End)