A026564 a(n) = Sum_{j=0..n} T(n, j), where T is given by A026552.

1, 2, 6, 11, 33, 64, 191, 376, 1122, 2222, 6636, 13180, 39395, 78373, 234414, 466840, 1397034, 2784266, 8335242, 16620976, 49773018, 99291358, 297406884, 593484440, 1777995535, 3548969075, 10633840743, 21230215328, 63620551947

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

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)/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}, Sum[T[n, k], {k,0,n}]];
Table[a[n], {n,0,40}] (* G. C. Greubel, Dec 19 2021 *)

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)
@CachedFunction
def a(n): return sum( T(n,k) for k in (0..n) )
[a(n) for n in (0..40)] # G. C. Greubel, Dec 19 2021

Formula

a(n) = Sum_{j=0..n} A026552(n, j).