A026745 a(n) = Sum_{j=0..n} Sum_{i=0..n} T(j,i), T given by A026736.

1, 3, 7, 15, 32, 66, 139, 285, 599, 1227, 2577, 5277, 11075, 22671, 47543, 97287, 203860, 417006, 873175, 1785513, 3736210, 7637604, 15972143, 32641221, 68224004, 139389570, 291199307, 594818781, 1242097912, 2536656174

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 (terms 0..1000 from G. C. Greubel)

Crossrefs

Cf. A026736.

Programs

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]];
b[n_]:= Sum[T[n, j], {j,0,n}]; Table[Sum[b[j], {j,0,n}], {n,0,35}] (* G. C. Greubel, Jul 22 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
def b(n): return sum(T(n, j) for j in (0..n))
[sum(b(j) for j in (0..n)) for n in (0..35)] # G. C. Greubel, Jul 22 2019

Formula

a(n) ~ c * phi^(3*n/2), where c = 1/2 + 3*phi^2 / (2*sqrt(5)) if n is even, c = 3*phi^(5/2) / (2*sqrt(5)) if n is odd and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jul 22 2019