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

0,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A026536, A026550, A027271.

Sequence in context: A119561 A228015 A145931 * A100098 A127361 A376489

Adjacent sequences: A026545 A026546 A026547 * A026549 A026550 A026551

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved