A027065 - OEIS

%I #11 Nov 07 2019 08:28:17

%S 0,2,6,20,68,230,776,2604,8670,28606,93494,302748,971810,3094486,

%T 9782092,30721056,95919714,297938906,921183940,2836545972,8702745304,

%U 26614653494,81159163058,246855070144,749123740876,2268700324802

%N a(n) = A027052(n, 2n-9).

%H G. C. Greubel, <a href="/A027065/b027065.txt">Table of n, a(n) for n = 5..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-9), n=5..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-9], {n,5,30}] (* _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-9) for n in (5..30)] # _G. C. Greubel_, Nov 06 2019

%K nonn

%O 5,2

%A _Clark Kimberling_