A027221 Sum of squares of numbers in row n of array T given by A026736.

1, 2, 6, 20, 79, 284, 1237, 4542, 20626, 76406, 354080, 1317964, 6173634, 23051344, 108628550, 406513364, 1922354351, 7206349304, 34147706833, 128187589014, 608151037123, 2285559568866, 10850577045131, 40817923301712, 193850277807569, 729825857819924, 3466587141136257

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026736.

Programs

GAP

T:= function(n, k)
    if k=0 or k=n then return 1;
    elif k=n-1 then return n;
    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);
    else return T(n-1, k-1) + T(n-1, k);
    fi;
  end;
List([0..21], n-> Sum([0..n], k-> T(n, k)^2 )); # G. C. Greubel, Jul 19 2019

Mathematica

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 *)

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) ));
vector(21, n, n--; sum(k=0, n, T(n, k)^2 ) ) \\ G. C. Greubel, Jul 19 2019

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    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)
    else: return T(n-1, k-1) + T(n-1, k)
[sum(T(n,k)^2 for k in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 19 2019