A027074 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027052.

1, 1, 4, 22, 93, 389, 1570, 6144, 23629, 89551, 335430, 1244762, 4583293, 16765087, 60980096, 220724896, 795540601, 2856541663, 10222762962, 36475315442, 129796579409, 460757642587, 1632012075912, 5768986242408

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..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-1), n=1..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-1}], {n, 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-1)) for n in (1..30)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A096167 A060453 A038382 * A036922 A340748 A036926

Adjacent sequences: A027071 A027072 A027073 * A027075 A027076 A027077

Keyword

nonn

Author

Clark Kimberling

Status

approved