A027275 - OEIS

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A027275

a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A026552.

24, 232, 954, 8560, 33648, 297940, 1159844, 10242416, 39809076, 351561242, 1367463642, 12086555584, 47082494816, 416589513644, 1625447736120, 14397549291280, 56265306436584, 498879779964188, 1952476424575980, 17327820010494464, 67907006619888744

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OFFSET

3,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 3..1000

FORMULA

a(n) = Sum_{k=0..2*n-3} A026552(n, k) * A026552(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)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)

a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}]];

Table[a[n], {n, 3, 40}] (* G. C. Greubel, Dec 18 2021 *)

PROG

(Sage)

@CachedFunction

def T(n, k): # T = A026552

if (k==0 or k==2*n): return 1

elif (k==1 or k==2*n-1): return (n+2)//2

elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)

else: return T(n-1, k) + T(n-1, k-2)

@CachedFunction

def a(n): return sum( T(n, k)*T(n, k+3) for k in (0..2*n-3) )