A026566 a(n) = Sum{T(i,j)}, 0<=j<=i, 0<=i<=n, T given by A026552.

1, 3, 9, 20, 53, 117, 308, 684, 1806, 4028, 10664, 23844, 63239, 141612, 376026, 842866, 2239900, 5024166, 13359408, 29980384, 79753402, 179044760, 476451644, 1069936084, 2847931619, 6396900694, 17030741437, 38260956765

Offset

0,2

Links

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

Formula

a(n) = Sum_{i=0..n} Sum_{j=0..i} A026552(i, 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[i, j], {i, 0, n}, {j, 0, i}]];
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( sum( T(i, j) for j in (0..i) ) for i 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, A026564, A026567, A027272, A027273, A027274, A027275, A027276.

Sequence in context: A220770 A191527 A226106 * A147356 A147416 A078841

Adjacent sequences: A026563 A026564 A026565 * A026567 A026568 A026569

Keyword

nonn

Author

Clark Kimberling

Status

approved