A026556 a(n) = T(n, n-3), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 3.

1, 3, 8, 24, 52, 156, 319, 954, 1910, 5696, 11304, 33648, 66514, 197778, 390266, 1159844, 2286996, 6795576, 13397075, 39809076, 78489235, 233262931, 460030947, 1367463642, 2697786052, 8021305890, 15830906756, 47082494816

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A026552, A026553, A026554, A026555, 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-3], {n,3,40}] (* 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-3) for n in (3..40)] # G. C. Greubel, Dec 17 2021

Formula

a(n) = A026552(n, n-3).