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%I #15 Oct 25 2019 16:50:54
%S 1,2,6,20,79,284,1237,4542,20626,76406,354080,1317964,6173634,
%T 23051344,108628550,406513364,1922354351,7206349304,34147706833,
%U 128187589014,608151037123,2285559568866,10850577045131,40817923301712,193850277807569,729825857819924,3466587141136257
%N Sum of squares of numbers in row n of array T given by A026736.
%H G. C. Greubel, <a href="/A027221/b027221.txt">Table of n, a(n) for n = 0..1000</a>
%t 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[Sum[T[n, k]^2, {k,0,n}], {n,0,40}] (* _G. C. Greubel_, Jul 19 2019 *)
%o (PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, 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 vector(21, n, n--; sum(k=0, n, T(n, k)^2 ) ) \\ _G. C. Greubel_, Jul 19 2019
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (k==0 or k==n): return 1
%o 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 else: return T(n-1, k-1) + T(n-1, k)
%o [sum(T(n,k)^2 for k in (0..n)) for n in (0..40)] # _G. C. Greubel_, Jul 19 2019
%o (GAP)
%o T:= function(n, k)
%o if k=0 or k=n then return 1;
%o elif k=n-1 then return n;
%o 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 else return T(n-1, k-1) + T(n-1, k);
%o fi;
%o end;
%o List([0..21], n-> Sum([0..n], k-> T(n, k)^2 )); # _G. C. Greubel_, Jul 19 2019
%Y Cf. A026736.
%K nonn
%O 0,2
%A _Clark Kimberling_
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