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

0,2

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A135048 A189319 A268501 * A243794 A318199 A242791

Adjacent sequences: A026561 A026562 A026563 * A026565 A026566 A026567

Keyword

nonn

Author

Clark Kimberling

Status

approved