A026593 a(n) = T(2*n-1, n-1), where T is given by A026584.

1, 1, 8, 22, 121, 406, 2155, 7624, 40717, 147001, 792351, 2892044, 15703156, 57728737, 315180458, 1164727748, 6385672193, 23691834033, 130316812494, 485018155062, 2674846358141, 9980763478121, 55161813337474, 206262229900060, 1142020843590221, 4277853480389546, 23721423518350124, 88991782850212510

Offset

1,3

Links

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

Formula

a(n) = A026584(2*n-1, n-1).

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n-1, n-1]];
Table[a[n], {n, 1, 40}] (* G. C. Greubel, Dec 13 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k):  # T = A026584
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n//2)
    else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
[T(2*n-1, n-1) for n in (1..40)] # G. C. Greubel, Dec 13 2021

Crossrefs

Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.

Sequence in context: A322070 A033456 A264631 * A131622 A217275 A183308

Adjacent sequences: A026590 A026591 A026592 * A026594 A026595 A026596

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(19) onward added by G. C. Greubel, Dec 13 2021

Status

approved