A027218 a(n) = Sum_{k=0..n-3} T(n,k)*T(n,k+3), T given by A026736.

1, 9, 51, 279, 1277, 6235, 26789, 125370, 525082, 2409886, 9969722, 45289767, 186105280, 840402559, 3439358196, 15472942142, 63155131233, 283400162019

Offset

3,2

Links

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

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]]; Table[Sum[T[n, k]*T[n, k+3], {k, 0, n-3}], {n, 3, 30}] (* G. C. Greubel, Jul 19 2019 *)

Prog

(PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, if((n%2)==0 && k==(n-2)/2, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
for(n=3, 20, print1(sum(k=0, n-3, T(n, k)*T(n, k+3)), ", ")) \\ G. C. Greubel, Jul 19 2019
(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1)
+ T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
[sum(T(n, k)*T(n, k+3) for k in (0..n-3)) for n in (3..30)] # G. C. Greubel, Jul 19 2019
(GAP)
T:= function(n, k)
    if k=0 or k=n then return 1;
    elif k=n-1 then return n;
    elif (n mod 2)=0 and k=Int((n-2)/2) then return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k);
    else return T(n-1, k-1) + T(n-1, k);
    fi;
  end;
List([3..20], n-> Sum([0..n-3], k-> T(n, k)*T(n, k+3) )); # G. C. Greubel, Jul 19 2019

Crossrefs

Cf. A026736.

Sequence in context: A080624 A125319 A080621 * A155617 A126477 A275861

Adjacent sequences: A027215 A027216 A027217 * A027219 A027220 A027221

Keyword

nonn

Author

Clark Kimberling

Status

approved