A210460 - OEIS

%I #18 Sep 08 2022 08:46:01

%S 1,2,4,10,23,53,123,285,660,1529,3542,8205,19007,44030,101996,236275,

%T 547334,1267906,2937120,6803875,15761261,36511157,84578549,195927260,

%U 453867933,1051390708,2435559643,5642004185,13069772820,30276291184

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

%C Transform of Fibonacci numbers based on the triangle A030528.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,2,1).

%F a(n) = sum(Fibonacci(k)*binomial(k,n-k), k=floor((n-1)/2)+1..n).

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

%F a(n) = A123392(n-1)+A123392(n-2). [_Bruno Berselli_, Jan 23 2013]

%t CoefficientList[Series[(1 + x)/(1 - x - 2 x^2 - 2 x^3 - x^4), {x, 0, 30}], x] (* _Bruno Berselli_, Jan 23 2013 *)

%t LinearRecurrence[{1,2,2,1},{1,2,4,10},30] (* _Harvey P. Dale_, Mar 28 2015 *)

%o (Magma) [&+[Fibonacci(k)*Binomial(k,n-k): k in [Floor((n-1)/2)+1..n]]: n in [1..30]]; // _Bruno Berselli_, Jan 23 2013

%Y Cf. A000045, A030528, A123392.

%K nonn,easy

%O 1,2

%A _Perminova Maria_, Jan 22 2013