A027038 - OEIS

%I #11 Nov 06 2019 08:47:31

%S 1,1,2,5,7,18,43,103,264,687,1809,4836,13049,35493,97218,267857,

%T 741791,2063574,5763595,16155403,45429488,128121191,362287433,

%U 1026918632,2917313257,8304598593,23685134746,67669857661,193652803391

%N Diagonal sum of right-justified array T given by A027023.

%H G. C. Greubel, <a href="/A027038/b027038.txt">Table of n, a(n) for n = 0..750</a>

%F a(n) = Sum_{k=0..n} T(n-k, 2*n-3*k), where T = A027023. - _G. C. Greubel_, Nov 05 2019

%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,2*n-3*k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 05 2019

%t T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n-k, 2*n-3*k], {k, 0, n}], {n, 0, 30}] (* _G. C. Greubel_, Nov 05 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, 2*n-3*k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Nov 05 2019

%K nonn

%O 0,3

%A _Clark Kimberling_