A027073 a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027052.

1, 1, 2, 8, 31, 129, 510, 1970, 7513, 28253, 105176, 388330, 1423691, 5188577, 18812848, 67907520, 244160177, 874821817, 3124747792, 11130097846, 39544807851, 140180597013, 495886522916, 1750852227736, 6171019594129

Offset

0,3

Links

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

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif k=0 or k=2 or k=2*n then 1
    elif k=1 then 0
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq( add(T(n, k)*T(n, 2*n-k), k=0..n), n=0..30); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n, k]*T[n, 2*n - k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Nov 06 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2 or k==2*n): return 1
    elif (k==1): return 0
    else: return sum(T(n-1, k-j) for j in (1..3))
[sum(T(n, k)*T(n, 2*n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A018916 A281831 A206229 * A150793 A150794 A150795

Adjacent sequences: A027070 A027071 A027072 * A027074 A027075 A027076

Keyword

nonn

Author

Clark Kimberling

Status

approved