A027218 a(n) = Sum_{k=0..n-3} T(n,k)*T(n,k+3), T given by A026736.

1, 9, 51, 279, 1277, 6235, 26789, 125370, 525082, 2409886, 9969722, 45289767, 186105280, 840402559, 3439358196, 15472942142, 63155131233, 283400162019

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..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([3..20], n-> Sum([0..n-3], k-> T(n, k)*T(n,k+3) )); # 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]*T[n,k+3], {k, 0, n-3}], {n, 3, 30}] (* 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) ));
for(n=3,20, print1(sum(k=0, n-3, T(n, k)*T(n,k+3)), ", ")) \\ 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)*T(n,k+3) for k in (0..n-3)) for n in (3..30)] # G. C. Greubel, Jul 19 2019