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A027063 a(n) = A027052(n, 2n-7).

%I A027063 #11 Nov 06 2019 04:27:53
%S A027063 0,2,6,20,68,228,754,2456,7884,24982,78282,242998,748364,2289584,
%T A027063 6966346,21098366,63651808,191406976,573998990,1717334182,5127933348,
%U A027063 15286303526,45503354154,135287179508,401809091392,1192336418386
%N A027063 a(n) = A027052(n, 2n-7).
%H A027063 G. C. Greubel, <a href="/A027063/b027063.txt">Table of n, a(n) for n = 4..750</a>
%p A027063 T:= proc(n, k) option remember;
%p A027063       if k<0 or k>2*n then 0
%p A027063     elif k=0 or k=2 or k=2*n then 1
%p A027063     elif k=1 then 0
%p A027063     else add(T(n-1, k-j), j=1..3)
%p A027063       fi
%p A027063     end:
%p A027063 seq( T(n,2*n-7), n=4..30); # _G. C. Greubel_, Nov 06 2019
%t A027063 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-7], {n,4,30}] (* _G. C. Greubel_, Nov 06 2019 *)
%o A027063 (Sage)
%o A027063 @CachedFunction
%o A027063 def T(n, k):
%o A027063     if (k<0 or k>2*n): return 0
%o A027063     elif (k==0 or k==2 or k==2*n): return 1
%o A027063     elif (k==1): return 0
%o A027063     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027063 [T(n,2*n-7) for n in (4..30)] # _G. C. Greubel_, Nov 06 2019
%K A027063 nonn
%O A027063 4,2
%A A027063 _Clark Kimberling_