A026550 a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026536.

1, 2, 6, 13, 35, 77, 204, 453, 1199, 2675, 7089, 15855, 42070, 94228, 250269, 561068, 1491262, 3345334, 8896310, 19966310, 53118352, 119257668, 317373194, 712742108, 1897253203, 4261711183, 11346582851, 25491926511, 67882263130

Offset

0,2

Links

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

Formula

a(n) = Sum_{j=0..n} Sum_{k=0..j} A026548(j, 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]] ]];
A026550[n_]:= A026550[n]= Sum[T[j, k], {j, 0, n}, {k, 0, j}];
Table[A026550[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 A026550(n): return sum(sum(T(j, k) for k in (0..j)) for j in (0..n))
[A026550(n) for n in (0..40)] # G. C. Greubel, Apr 12 2022

Crossrefs

Cf. A026548.

Sequence in context: A116426 A196906 A162057 * A319751 A124124 A052450

Adjacent sequences: A026547 A026548 A026549 * A026551 A026552 A026553

Keyword

nonn

Author

Clark Kimberling

Status

approved