A027068 - OEIS

%I #17 Nov 07 2019 08:28:07

%S 1,2,6,16,43,120,340,972,2793,8050,23256,67324,195275,567448,1651830,

%T 4816328,14064569,41128626,120425604,353022920,1035983443,3043189688,

%U 8947381566,26328236756,77531471737,228475334594,673725464150

%N a(n) = Sum_{i=0..n} Sum_{j=i..2*i} A027052(i, j).

%H G. C. Greubel, <a href="/A027068/b027068.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(add(T(k,j), j=k..2*k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 06 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[Sum[T[i, j], {j, i, 2*i}], {i, 0, n}], {n,0,30}] (* _G. C. Greubel_, Nov 06 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(sum(T(k,j) for j in (k..2*k)) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Nov 06 2019

%Y Cf. A027052. Partial sums of A027067.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E Title corrected by _Sean A. Irvine_, Oct 22 2019