|
%I #9 Oct 18 2021 16:26:44
%S 1,2,5,14,39,106,283,748,1967,5160,13521,35412,92725,242774,635609,
%T 1664066,4356603,11405758,29860687,78176320,204668291,535828572,
%U 1402817445,3672623784,9615053929,25172538026,65902560173,172535142518
%N a(n) = Sum_{k=0..n} ( Fibonacci(2*k-1) + (n-k)*Fibonacci(2*k) ).
%C Row sums of triangle A141751.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,5,-1).
%F G.f.: (1 - 3*x + 3*x^2)/((1 - 3*x + x^2)*(1-x)^2).
%F a(n) = A055588(n) + A054452(n). - _R. J. Mathar_, Apr 16 2016
%F a(n) = 5*a(n-1)-8*a(n-2)+5*a(n-3)-a(n-4). - _Wesley Ivan Hurt_, Oct 18 2021
%t LinearRecurrence[{5,-8,5,-1},{1,2,5,14},30] (* _Harvey P. Dale_, May 23 2021 *)
%o (PARI) a(n)=sum(k=0,n,fibonacci(2*k-1) + (n-k)*fibonacci(2*k))
%Y Cf. A054452, A055588, A141751.
%K nonn,easy
%O 0,2
%A _Paul D. Hanna_, Jul 04 2008
|
