A026554 a(n) = T(n,n-1), T given by A026552. Also a(n) is the number of integer strings s(0),...,s(n) counted by T, such that s(n)=1.

1, 2, 4, 10, 19, 52, 98, 278, 526, 1516, 2887, 8389, 16073, 46936, 90386, 264842, 512128, 1504432, 2918954, 8592094, 16716998, 49288856, 96119927, 283795571, 554524660, 1639174304, 3208254571, 9493241125, 18607536319, 55108565584

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A026520(n+1)/2.

Mathematica

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

Prog

(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-1) for n in (1..40)] # G. C. Greubel, Dec 17 2021

Crossrefs

Cf. A026520.

Cf. A026552, A026553, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

Sequence in context: A263738 A011963 A083844 * A259132 A369391 A099413

Adjacent sequences: A026551 A026552 A026553 * A026555 A026556 A026557

Keyword

nonn

Author

Clark Kimberling

Status

approved