A352972 - OEIS

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

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OFFSET

0,2

LINKS

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

FORMULA

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

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

Table[A352972[n], {n, 0, 40}]

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 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)]