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A027031 a(n) = T(n,2n-7), T given by A027023.

%I A027031 #8 Nov 05 2019 07:23:30
%S A027031 1,3,9,31,105,351,1157,3755,12013,37951,118613,367383,1129345,3449823,
%T A027031 10482869,31713863,95589753,287224199,860773781,2573894583,7681972113,
%U A027031 22890634939,68116073369,202458285647,601159897137
%N A027031 a(n) = T(n,2n-7), T given by A027023.
%H A027031 G. C. Greubel, <a href="/A027031/b027031.txt">Table of n, a(n) for n = 4..750</a>
%p A027031 T:= proc(n, k) option remember;
%p A027031       if k<3 or k=2*n then 1
%p A027031     else add(T(n-1, k-j), j=1..3)
%p A027031       fi
%p A027031     end:
%p A027031 seq(T(n,2*n-7), n=4..30); # _G. C. Greubel_, Nov 05 2019
%t A027031 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[T[n, 2*n-7], {n,4,30}] (* _G. C. Greubel_, Nov 05 2019 *)
%o A027031 (Sage)
%o A027031 @CachedFunction
%o A027031 def T(n, k):
%o A027031     if (k<3 or k==2*n): return 1
%o A027031     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027031 [T(n, 2*n-7) for n in (4..30)] # _G. C. Greubel_, Nov 05 2019
%K A027031 nonn
%O A027031 4,2
%A A027031 _Clark Kimberling_