A026555 a(n) = T(n, n-2), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 2.

1, 2, 7, 13, 40, 76, 226, 434, 1279, 2470, 7267, 14085, 41462, 80584, 237484, 462620, 1365014, 2664276, 7870226, 15387670, 45501743, 89097932, 263707094, 517058502, 1531614109, 3006637946, 8912678569, 17514547015, 51952990090

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A026552, A026553, A026554, 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-2], {n,2,40}] (* 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-2) for n in (1..40)] # G. C. Greubel, Dec 17 2021

Formula

a(n) = A026552(n, n-2).