A026526 a(n) = T(2n,n-1), T given by A026519.

1, 2, 9, 32, 130, 516, 2107, 8632, 35703, 148390, 619850, 2598960, 10933507, 46124274, 195055005, 826617216, 3509650697, 14926011714, 63572290247, 271125967840, 1157705297385, 4948808238110, 21175676836110, 90692557152240, 388751132082600, 1667665994149376, 7159105163384127, 30753762496639504

Offset

1,2

Links

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

Formula

a(n) = A026519(2*n, n-1).

a(n) = A026536(2*n, n-1).

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-1] ];
Table[a[n], {n, 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-1) for n in (1..40)] # G. C. Greubel, Dec 20 2021

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026527, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.

Cf. A026536.

Sequence in context: A006253 A045630 A075364 * A086607 A150913 A150914

Adjacent sequences: A026523 A026524 A026525 * A026527 A026528 A026529

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved