A026557 a(n) = T(n, n-4), T given by A026552. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.

1, 3, 12, 28, 93, 201, 631, 1316, 4037, 8259, 25052, 50680, 152782, 306958, 921982, 1844304, 5526849, 11024331, 32987492, 65675764, 196323853, 390374193, 1166171943, 2316881892, 6918228187, 13737041045, 41007165500

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026558, A026559, A026560, 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-4], {n,4,40}] (* 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-4) for n in (4..40)] # G. C. Greubel, Dec 17 2021

Formula

a(n) = A026552(n, n-4).