OFFSET
2,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..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+2], {k, 0, n-2}], {n, 2, 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) ));
vector(20, n, n++; sum(k=0, n-2, T(n, k)*T(n, k+2)) ) \\ 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+2) for k in (0..n-2)) for n in (2..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([2..20], n-> Sum([0..n-2], k-> T(n, k)*T(n, k+2) )); # G. C. Greubel, Jul 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved