A027283 - OEIS

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A027283

a(n) = Sum_{k=0..2*n-1} T(n,k) * T(n,k+1), with T given by A026584.

0, 6, 26, 206, 1100, 7314, 42920, 274010, 1677332, 10616070, 66290046, 419754586, 2648500908, 16818685050, 106781976774, 680250643910, 4337083126232, 27709045093274, 177213890858938, 1135003956744310, 7276652578220372, 46702733068082702, 300013046145979184

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{k=0..2*n-1} A026584(n,k) * A026584(n,k+1).

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+1], {k, 0, 2*n-1}];

Table[a[n], {n, 1, 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 A027283(n): return sum(T(n, j)*T(n, j+1) for j in (0..2*n-1))

[A027283(n) for n in (1..40)] # G. C. Greubel, Dec 15 2021