A026525 a(n) = T(2*n, n), where T is given by A026519.

1, 1, 5, 16, 65, 251, 1016, 4117, 16913, 69865, 290455, 1212905, 5085224, 21389824, 90226449, 381519416, 1616684241, 6863544233, 29187402749, 124305180842, 530108333515, 2263423401745, 9674857844129, 41396075156859, 177285394355336, 759895396193376, 3259667597627576, 13992851410449865

Offset

0,3

Links

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

Formula

a(n) = A026519(2*n, n).

a(n) = A026536(2*n, n).

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/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 = A026519 *)
a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, T[2 n, n] ];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 20 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k): # T = A026519
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+1)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
[T(2*n, n) for n in (0..40)] # G. C. Greubel, Dec 20 2021

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026526, A026527, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.

Cf. A026536.

Sequence in context: A275100 A301958 A349568 * A007043 A128242 A323934

Adjacent sequences: A026522 A026523 A026524 * A026526 A026527 A026528

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(20) onward added by G. C. Greubel, Dec 20 2021

Status

approved