A027045 - OEIS

%I #25 Sep 08 2022 08:44:49

%S 1,4,11,34,103,306,901,2636,7685,22372,65111,189590,552547,1612154,

%T 4709369,13773368,40329465,118217992,346891115,1018872626,2995250535,

%U 8812601062,25948130525,76456539156,225427875325,665066293480

%N a(n) = Sum_{k=n+1..2*n} T(n, k), T given by A027023.

%H G. C. Greubel, <a href="/A027045/b027045.txt">Table of n, a(n) for n = 1..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), k=n+1..2*n), n=1..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], {k,n+1,2*n}], {n,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) for k in (n+1..2*n)) for n in (1..30)] # _G. C. Greubel_, Nov 04 2019

%o (Magma) function T(n,k)

%o   if k lt 3 or k eq 2*n then return 1;

%o   else return (&+[T(n-1,k-j): j in [1..3]]);

%o   end if; return T; end function;

%o [(&+[T(n,k): k in [n+1..2*n]]): n in [1..15]]; // _G. C. Greubel_, Nov 20 2019

%Y Cf. A027023.

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Offset changed by _G. C. Greubel_, Nov 04 2019