cp's OEIS Frontend

A027037 Diagonal sum of left-justified array T given by A027023.

%I A027037 #14 Nov 06 2019 01:02:41
%S A027037 1,1,2,3,3,6,7,11,16,21,33,48,65,101,146,203,311,450,635,963,1396,
%T A027037 1989,2993,4348,6233,9329,13574,19543,29135,42446,61303,91123,132884,
%U A027037 192377,285309,416384,603925,894069,1305618,1896495,2803611,4096182,5957183,8796287
%N A027037 Diagonal sum of left-justified array T given by A027023.
%H A027037 G. C. Greubel, <a href="/A027037/b027037.txt">Table of n, a(n) for n = 0..1000</a>
%F A027037 a(n) = Sum_{k=0..n} A027023(n-k, k). - _Sean A. Irvine_, Oct 22 2019
%p A027037 T:= proc(n, k) option remember;
%p A027037       if n<0 or k>2*n then 0
%p A027037     elif k<3 or k=2*n then 1
%p A027037     else add(T(n-1, k-j), j=1..3)
%p A027037       fi
%p A027037     end:
%p A027037 seq( add(T(n-k,k), k=0..n), n=0..30); # _G. C. Greubel_, Nov 05 2019
%t A027037 T[n_, k_]:= T[n, k]= If[n<0 || k>2*n, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n-k, k], {k, 0, n}], {n,0,30}] (* _G. C. Greubel_, Nov 05 2019 *)
%o A027037 (Sage)
%o A027037 @CachedFunction
%o A027037 def T(n, k):
%o A027037     if (n<0 or k>2*n): return 0
%o A027037     elif (k<3 or k==2*n): return 1
%o A027037     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027037 [sum(T(n-k, k) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, Nov 05 2019
%K A027037 nonn
%O A027037 0,3
%A A027037 _Clark Kimberling_
%E A027037 More terms from _Sean A. Irvine_, Oct 21 2019