A027060 - OEIS

%I #8 Nov 06 2019 04:27:17

%S 1,1,3,11,35,107,319,935,2713,7825,22491,64523,184945,530001,1519151,

%T 4356471,12501301,35901325,103188123,296844379,854701935,2463133311,

%U 7104685935,20510632575,59262772629,171373598341,495968905267

%N a(n) = T(n,2n-4), T given by A027052.

%H G. C. Greubel, <a href="/A027060/b027060.txt">Table of n, a(n) for n = 2..750</a>

%p T:= proc(n, k) option remember;

%p       if k<0 or k>2*n then 0

%p     elif k=0 or k=2 or k=2*n then 1

%p     elif k=1 then 0

%p     else add(T(n-1, k-j), j=1..3)

%p       fi

%p     end:

%p seq( T(n,2*n-4), n=2..30); # _G. C. Greubel_, Nov 06 2019

%t T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[T[n,2*n-4], {n,2,30}] (* _G. C. Greubel_, Nov 06 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o     if (k<0 or k>2*n): return 0

%o     elif (k==0 or k==2 or k==2*n): return 1

%o     elif (k==1): return 0

%o     else: return sum(T(n-1, k-j) for j in (1..3))

%o [T(n,2*n-4) for n in (2..30)] # _G. C. Greubel_, Nov 06 2019

%K nonn

%O 2,3

%A _Clark Kimberling_