OFFSET
1,3
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).
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)
MATHEMATICA
LinearRecurrence[{2, -1, 2}, {1, 1, 2}, 31] (* Ray Chandler, Sep 23 2015 *)
PROG
(Magma) [Round(3*2^(n-1)/5): n in [1..41]]; // G. C. Greubel, Jul 08 2022
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved