A352972 a(n) = Sum_{j=0..2*n} Sum_{k=0..j} A026536(j, k).

1, 6, 35, 204, 1199, 7089, 42070, 250269, 1491262, 8896310, 53118352, 317373194, 1897253203, 11346582851, 67882263130, 406231442387, 2431626954934, 14558306758418, 87177151134954, 522110098886882, 3127380060424476, 18734897945679836, 112245303177542790, 672552484035697364, 4030148584900522009

Offset: 0

Author

G. C. Greubel, Apr 12 2022

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A026536, A026550.

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], 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]] ]];
A352972[n_]:= A352972[n]= Sum[T[j,k], {j,0,2*n}, {k,0,j}];
Table[A352972[n], {n,0,40}]

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 A352972(n): return sum(sum(T(j,k) for k in (0..j)) for j in (0..2*n))
[A352972(n) for n in (3..40)]

Formula

a(n) = Sum_{j=0..2*n} Sum_{k=0..j} A026536(j, k).