A027046 - OEIS

%I #15 Nov 05 2019 05:55:31

%S 1,2,5,16,65,286,1305,6232,30377,150178,750937,3785904,19215865,

%T 98086646,503087741,2591128000,13394476993,69466312210,361315132065,

%U 1884242109256,9849626540337,51599350440694,270851460356973

%N a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027023.

%H G. C. Greubel, <a href="/A027046/b027046.txt">Table of n, a(n) for n = 0..1000</a>

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

%p       if k<3 or k=2*n then 1

%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 04 2019

%t T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[T[n,k]*T[n,n+k], {k,0,n}], {n,0,30}] (* _G. C. Greubel_, Nov 04 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o     if (k<3 or k==2*n): return 1

%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 04 2019

%K nonn

%O 0,2

%A _Clark Kimberling_