cp's OEIS Frontend

A027038 Diagonal sum of right-justified array T given by A027023.

%I A027038 #15 Aug 09 2025 06:12:56
%S A027038 1,1,2,5,7,18,43,103,264,687,1809,4836,13049,35493,97218,267857,
%T A027038 741791,2063574,5763595,16155403,45429488,128121191,362287433,
%U A027038 1026918632,2917313257,8304598593,23685134746,67669857661,193652803391
%N A027038 Diagonal sum of right-justified array T given by A027023.
%H A027038 G. C. Greubel, <a href="/A027038/b027038.txt">Table of n, a(n) for n = 0..750</a>
%F A027038 a(n) = Sum_{k=0..n} T(n-k, 2*n-3*k), where T = A027023. - _G. C. Greubel_, Nov 05 2019
%F A027038 a(n) ~ 3^(n + 7/2) / (16 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Aug 09 2025
%p A027038 T:= proc(n, k) option remember;
%p A027038       if k<3 or k=2*n then 1
%p A027038     else add(T(n-1, k-j), j=1..3)
%p A027038       fi
%p A027038     end:
%p A027038 seq( add(T(n-k,2*n-3*k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 05 2019
%t A027038 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 A027038 (Sage)
%o A027038 @CachedFunction
%o A027038 def T(n, k):
%o A027038     if (k<3 or k==2*n): return 1
%o A027038     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027038 [sum(T(n-k, 2*n-3*k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Nov 05 2019
%Y A027038 Cf. A027023.
%K A027038 nonn
%O A027038 0,3
%A A027038 _Clark Kimberling_