A111573 - OEIS

%I #32 Jan 16 2024 04:10:00

%S 0,1,3,3,4,8,14,21,33,55,90,144,232,377,611,987,1596,2584,4182,6765,

%T 10945,17711,28658,46368,75024,121393,196419,317811,514228,832040,

%U 1346270,2178309,3524577,5702887,9227466,14930352,24157816,39088169

%N a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.

%C See comment and FAMP code for A111569.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1).

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

%F a(n) = A056594(n+3) + A000045(n+1). - _R. J. Mathar_, Nov 10 2009

%F From _Greg Dresden_, Jan 15 2024: (Start)

%F a(2*n) = Fibonacci(n)*Lucas(n+1);

%F a(2*n+1) = Fibonacci(2*n+1). (End)

%t Table[Fibonacci[n + 1] - Cos[n*Pi/2], {n, 0, 40}] (* _Greg Dresden_, Oct 16 2021 *)

%Y Cf. A001638, A111569, A111570, A111571, A111572, A111574, A111575, A111576.

%K easy,nonn

%O 0,3

%A _Creighton Dement_, Aug 10 2005