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

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) )
[a(n) for n in (3..40)] # G. C. Greubel, Dec 18 2021

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A026567, A027272, A027273, A027274, A027276.

Sequence in context: A345648 A022684 A297752 * A027260 A125387 A126545

Adjacent sequences: A027272 A027273 A027274 * A027276 A027277 A027278

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved