A027049 - OEIS

%I #12 Nov 04 2019 19:39:15

%S 16,120,952,7848,65580,550476,4631876,39047764,329784608,2790469092,

%T 23656401612,200928615160,1709781846028,14575407966156,

%U 124466311279620,1064636218853556,9120848372291680,78256468639080460,672393605270681188,5785139333187494936,49838058776228021388

%N a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027023.

%H G. C. Greubel, <a href="/A027049/b027049.txt">Table of n, a(n) for n = 3..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,k+3), k=0..2*n-3), n=3..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,k+3], {k,0,2*n-3}], {n,3,30}] (* _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,k+3) for k in (0..2*n-3)) for n in (3..30)] # _G. C. Greubel_, Nov 04 2019

%K nonn

%O 3,1

%A _Clark Kimberling_

%E More terms from _Sean A. Irvine_, Oct 22 2019