A026553 a(n) = T(n,n), T given by A026552. Also a(n) is the number of integer strings s(0),...,s(n) counted by T, such that s(n)=0.

1, 1, 3, 4, 12, 20, 58, 104, 300, 556, 1608, 3032, 8806, 16778, 48924, 93872, 274644, 529684, 1553940, 3008864, 8846772, 17184188, 50618184, 98577712, 290817566, 567591142, 1676640462, 3278348608, 9694857750, 18986482250

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026552, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
Table[T[n,n], {n,0,40}] (* G. C. Greubel, Dec 17 2021 *)

Sage

@CachedFunction
def T(n,k): # T = A026552
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+2)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-2)
[T(n,n) for n in (0..40)] # G. C. Greubel, Dec 17 2021

Formula

a(n) = A026552(n,n).