A027049 a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027023.

16, 120, 952, 7848, 65580, 550476, 4631876, 39047764, 329784608, 2790469092, 23656401612, 200928615160, 1709781846028, 14575407966156, 124466311279620, 1064636218853556, 9120848372291680, 78256468639080460, 672393605270681188, 5785139333187494936, 49838058776228021388

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Programs

Maple

T:= proc(n, k) option remember;
      if k<3 or k=2*n then 1
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq(add(T(n,k)*T(n,k+3), k=0..2*n-3), n=3..30); # G. C. Greubel, Nov 04 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[T[n,k]*T[n,k+3], {k,0,2*n-3}], {n,3,30}] (* G. C. Greubel, Nov 04 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k<3 or k==2*n): return 1
    else: return sum(T(n-1, k-j) for j in (1..3))
[sum(T(n,k)*T(n,k+3) for k in (0..2*n-3)) for n in (3..30)] # G. C. Greubel, Nov 04 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019