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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

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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