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A027285
a(n) = Sum_{k=0..2*n-3} T(n,k) * T(n,k+3), with T given by A026584.
16
12, 116, 682, 4908, 30272, 201648, 1273286, 8275894, 52783298, 340392020, 2180905198, 14035736838, 90149817980, 580197442656, 3732734480794, 24041345351898, 154874693823022, 998441294531516, 6439238635990250, 41552345665859196, 268252644944872486
OFFSET
3,1
LINKS
FORMULA
a(n) = Sum_{k=0..2*n-3} A026584(n,k) * A026584(n,k+3).
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+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}];
Table[a[n], {n, 3, 40}] (* G. C. Greubel, Dec 15 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026584
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
@CachedFunction
def A027285(n): return sum(T(n, j)*T(n, j+3) for j in (0..2*n-3))
[A027285(n) for n in (3..40)] # G. C. Greubel, Dec 15 2021
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 26 2019
STATUS
approved