A027078 - OEIS

%I #13 Nov 07 2019 14:48:45

%S 1,0,2,8,31,130,590,2798,13541,66724,332708,1673536,8479367,43218034,

%T 221383712,1138976166,5882112985,30479772624,158413903096,

%U 825556260636,4312814257059,22580855859166,118468635595680,622698941708890

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

%H G. C. Greubel, <a href="/A027078/b027078.txt">Table of n, a(n) for n = 0..1000</a>

%p T:= proc(n, k) option remember;

%p       if k<0 or k>2*n then 0

%p     elif k=0 or k=2 or k=2*n then 1

%p     elif k=1 then 0

%p     else add(T(n-1, k-j), j=1..3)

%p       fi

%p     end:

%p seq( add(T(n,k)*T(n,n+k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 07 2019

%t 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 (Sage)

%o @CachedFunction

%o def T(n, k):

%o     if (k<0 or k>2*n): return 0

%o     elif (k==0 or k==2 or k==2*n): return 1

%o     elif (k==1): return 0

%o     else: return sum(T(n-1, k-j) for j in (1..3))

%o [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 nonn

%O 0,3

%A _Clark Kimberling_