|
%I #16 Sep 08 2022 08:45:57
%S 0,2,8,48,258,1518,8910,53526,323796,1976876,12138456,74921904,
%T 464320368,2887660168,18011618368,112633305568,705899650498,
%U 4432668783838,27882818399038,175661366346838,1108193133814138,6999963827434378,44265660573879298
%N 1-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.
%C See A192232, A192250.
%F a(n) = 2*A192070(n).
%F Conjecture: (n-1)*(n-2)*a(n) -(5*n-7)*(n-2)*a(n-1) -2*(2*n-3)*(3*n-8)*a(n-2) +4*(2*n-3)*(2*n-5)*a(n-3)=0. - _R. J. Mathar_, May 04 2014
%F a(n) = Sum_{i=0..n-1} A000045(i)*binomial(2*i, i). - _John M. Campbell_, Feb 01 2016
%t (See A192250.)
%t Table[Sum[Fibonacci[i] Binomial[2 i, i], {i, 0, n - 1}], {n, 23}] (* _Michael De Vlieger_, Feb 01 2016 *)
%o (Magma) [&+[Fibonacci(k)*Binomial(2*k,k): k in [0..n]]: n in [0..28]]; // _Vincenzo Librandi_, Feb 04 2016
%Y Cf. A192232, A192250, A192070.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jun 27 2011
|
