A026559 a(n) = T(2*n, n-1), where T is given by A026552.

1, 3, 12, 45, 180, 721, 2940, 12069, 49935, 207691, 867900, 3640429, 15319395, 64643580, 273431408, 1158988141, 4921651521, 20934115963, 89173404140, 380355072153, 1624282578215, 6943928981859, 29715239620368, 127276313406125, 545605497876400, 2340694589348376, 10048952593607088, 43170264470594302

Offset

1,2

Links

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

Formula

a(n) = A026552(2*n, 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)/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[2*n, n-1]];
Table[a[n], {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(2*n, n-1) for n in (1..40)] # G. C. Greubel, Dec 17 2021

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026560, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

Sequence in context: A192467 A151162 A094547 * A188949 A184699 A008781

Adjacent sequences: A026556 A026557 A026558 * A026560 A026561 A026562

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(20) onward added by G. C. Greubel, Dec 17 2021

Status

approved