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A026742 a(n) = T(n, floor(n/2)), T given by A026736.

%I A026742 #15 Jul 19 2019 17:05:17
%S A026742 1,1,2,3,6,11,21,43,79,173,309,707,1237,2917,5026,12111,20626,50503,
%T A026742 85242,211263,354080,885831,1476368,3720995,6173634,15652239,25873744,
%U A026742 65913927,108628550,277822147,456710589,1171853635,1922354351
%N A026742 a(n) = T(n, floor(n/2)), T given by A026736.
%H A026742 G. C. Greubel, <a href="/A026742/b026742.txt">Table of n, a(n) for n = 0..1000</a>
%F A026742 a(n) ~ phi^(3*n/2 - (7 + (-1)^n)/4) / sqrt(5), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jul 19 2019
%t A026742 T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] +T[n-2, k-1] +T[n-1, k], T[n-1, k-1] + T[n-1, k]]]; Table[T[n, Floor[n/2]], {n,0,40}] (* _G. C. Greubel_, Jul 19 2019 *)
%o A026742 (PARI) T(n,k) = if(k==n || k==0, 1, if((n%2)==0 && k==(n-2)/2, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
%o A026742 vector(20, n, n--; T(n, n\2)) \\ _G. C. Greubel_, Jul 19 2019
%o A026742 (Sage) @CachedFunction
%o A026742 def T(n, k):
%o A026742     if (k==0 or k==n): return 1
%o A026742     elif (mod(n,2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
%o A026742     else: return T(n-1, k-1) + T(n-1, k)
%o A026742 [T(n, floor(n/2)) for n in (0..40)] # _G. C. Greubel_, Jul 19 2019
%o A026742 (GAP)
%o A026742 T:= function(n,k)
%o A026742     if k=0 or k=n then return 1;
%o A026742     elif (n mod 2)=0 and k=Int((n-2)/2) then return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k);
%o A026742     else return T(n-1, k-1) + T(n-1, k);
%o A026742     fi;
%o A026742   end;
%o A026742 Flat(List([0..20], n-> T(n,Int(n/2)) )); # _G. C. Greubel_, Jul 19 2019
%Y A026742 Cf. A026736.
%K A026742 nonn
%O A026742 0,3
%A A026742 _Clark Kimberling_