A026548 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026536.

1, 1, 4, 7, 22, 42, 127, 249, 746, 1476, 4414, 8766, 26215, 52158, 156041, 310799, 930194, 1854072, 5550976, 11070000, 33152042, 66139316, 198115526, 395368914, 1184511095, 2364457980, 7084871668, 14145343660, 42390336619

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026536, A026550, A027271.

Programs

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], T[n-1,k-2] +T[n-1,k-1] +T[n-1,k], T[n-1, k-2] +T[n-1,k]]]];
Table[Sum[T[n, k], {k,0,n}], {n,0,40}] (* G. C. Greubel, Apr 12 2022 *)

SageMath

@CachedFunction
def T(n, k): # A026536
    if k == 0 or k == 2*n: return 1
    elif k == 1 or k == 2*n-1: return n//2
    elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
    return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
def A026548(n): return sum(T(n,k) for k in (0..n))
[A026548(n) for n in (0..40)] # G. C. Greubel, Apr 12 2022

Formula

a(n) = Sum_{k=0..n} A026536(n, k).

Extensions

Missing a(0)=1 inserted by Sean A. Irvine, Oct 06 2019