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A027218
a(n) = Sum_{k=0..n-3} T(n,k)*T(n,k+3), T given by A026736.
1
1, 9, 51, 279, 1277, 6235, 26789, 125370, 525082, 2409886, 9969722, 45289767, 186105280, 840402559, 3439358196, 15472942142, 63155131233, 283400162019
OFFSET
3,2
LINKS
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
KEYWORD
nonn
STATUS
approved