A083862 - OEIS

%I #8 Dec 26 2019 04:46:12

%S 0,1,3,10,39,171,819,4229,23247,135088,824163,5255361,34876647,

%T 240130801,1710323667,12572548582,95183606559,740843916471,

%U 5918533467075,48463830575837,406239439253175,3481899731310196

%N Main diagonal of array A083857.

%F a(n) = (((3 + sqrt(4*n + 1))/2)^n - ((3 - sqrt(4*n + 1))/2)^n)/sqrt(4*n + 1).

%p T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := 3*T(n, k - 1) + (n - 2)*T(n, k - 2); end if; v; end proc;

%p seq(T(n, n), n = 0 .. 40); # _Petros Hadjicostas_, Dec 25 2019

%Y Cf. A083857, A083859, A083863.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 06 2003