A026563 a(n) = T(n, floor(n/2)), where T is given by A026552.

1, 1, 2, 2, 7, 8, 24, 28, 93, 111, 362, 436, 1452, 1763, 5880, 7176, 24089, 29521, 99386, 122182, 412637, 508595, 1721500, 2126312, 7211536, 8923136, 30312960, 37563930, 127790379, 158563368, 540082784, 670893296, 2287577537

Offset

0,3

Links

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

Formula

a(n) = A026552(n, floor(n/2)).

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 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[n, Floor[n/2]]];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 18 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//2) for n in (0..40)] # G. C. Greubel, Dec 18 2021

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

Sequence in context: A005300 A019087 A293607 * A062305 A155063 A324666

Adjacent sequences: A026560 A026561 A026562 * A026564 A026565 A026566

Keyword

nonn

Author

Clark Kimberling

Status

approved