A026530 a(n) = T(n, floor(n/2)), T given by A026519.

1, 1, 1, 2, 5, 8, 16, 28, 65, 111, 251, 436, 1016, 1763, 4117, 7176, 16913, 29521, 69865, 122182, 290455, 508595, 1212905, 2126312, 5085224, 8923136, 21389824, 37563930, 90226449, 158563368, 381519416, 670893296, 1616684241, 2844444761

Offset

0,4

Links

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

Formula

a(n) = A026519(n, floor(n/2)).

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[n, Floor[n/2]] ];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 21 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(n, n//2) for n in (0..40)] # G. C. Greubel, Dec 21 2021

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026531, A026532, A026533, A026534, A027262, A027263, A027264, A027265, A027266.

Sequence in context: A301596 A026007 A032233 * A336135 A032254 A323586

Adjacent sequences: A026527 A026528 A026529 * A026531 A026532 A026533

Keyword

nonn

Author

Clark Kimberling

Status

approved