A027048 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027023.

5, 29, 213, 1633, 12821, 102369, 826305, 6724933, 55108961, 454279229, 3764205941, 31334121045, 261903891425, 2197181330193, 18494163039793, 156140262436597, 1321876222268977, 11219183496737037, 95441562533950341, 813656964557564557, 6950294796825730249

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..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+2), k=0..2*n-2), n=2..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+2], {k,0,2*n-2}], {n,2,30}] (* 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+2) for k in (0..2*n-2)) for n in (2..30)] # G. C. Greubel, Nov 04 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019