cp's OEIS Frontend

A027078 a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027052.

%I A027078 #13 Nov 07 2019 14:48:45
%S A027078 1,0,2,8,31,130,590,2798,13541,66724,332708,1673536,8479367,43218034,
%T A027078 221383712,1138976166,5882112985,30479772624,158413903096,
%U A027078 825556260636,4312814257059,22580855859166,118468635595680,622698941708890
%N A027078 a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027052.
%H A027078 G. C. Greubel, <a href="/A027078/b027078.txt">Table of n, a(n) for n = 0..1000</a>
%p A027078 T:= proc(n, k) option remember;
%p A027078       if k<0 or k>2*n then 0
%p A027078     elif k=0 or k=2 or k=2*n then 1
%p A027078     elif k=1 then 0
%p A027078     else add(T(n-1, k-j), j=1..3)
%p A027078       fi
%p A027078     end:
%p A027078 seq( add(T(n,k)*T(n,n+k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 07 2019
%t A027078 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n, k]*T[n, n+k], {k, 0, n}], {n,30}] (* _G. C. Greubel_, Nov 07 2019 *)
%o A027078 (Sage)
%o A027078 @CachedFunction
%o A027078 def T(n, k):
%o A027078     if (k<0 or k>2*n): return 0
%o A027078     elif (k==0 or k==2 or k==2*n): return 1
%o A027078     elif (k==1): return 0
%o A027078     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027078 [sum(T(n,k)*T(n,n+k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Nov 07 2019
%K A027078 nonn
%O A027078 0,3
%A A027078 _Clark Kimberling_