cp's OEIS Frontend

A168148 Row sums of triangle in A168030.

%I A168148 #7 Jan 12 2023 04:12:47
%S A168148 1,1,2,2,3,4,4,3,6,6,6,4,6,7,10,6,11,12,10,6,8,8,12,8,12,11,18,12,13,
%T A168148 16,20,11,22,22,18,12,14,14,16,10,14,12,24,16,16,18,22,12,22,23,34,20,
%U A168148 25,28,26,17,30,26,38,24,26,31,42,22,43,44,34,22,28,26,30,20,26
%N A168148 Row sums of triangle in A168030.
%H A168148 G. C. Greubel, <a href="/A168148/b168148.txt">Table of n, a(n) for n = 0..5000</a>
%F A168148 From _G. C. Greubel_, Jan 12 2023: (Start)
%F A168148 a(n) = Sum_{k=0..n} A168030(n, k).
%F A168148 a(n) = Sum_{k=0..n} (A118340(n, k) mod 2). (End)
%t A168148 t[n_, k_]:= t[n, k]= If[k<0 || k>n, 0, If[k==0, 1, If[n<=2*k, t[n, n-k -1] + t[n-1,k], t[n,n-k] + t[n-1,k]]]]; (* A118340 *)
%t A168148 Table[Sum[Mod[t[n, k], 2], {k,0,n}], {n,0,80}] (* _G. C. Greubel_, Jan 12 2023 *)
%o A168148 (SageMath)
%o A168148 @CachedFunction
%o A168148 def t(n, k): # t = A118340
%o A168148     if (k<0 or k>n): return 0
%o A168148     elif (k==0): return 1
%o A168148     elif (n>2*k): return t(n, n-k) + t(n-1, k)
%o A168148     else: return t(n, n-k-1) + t(n-1, k)
%o A168148 def A168148(n): return sum( t(n,k)%2 for k in range(n+1))
%o A168148 [A168148(n) for n in range(81)] # _G. C. Greubel_, Jan 12 2023
%Y A168148 Cf. A118340, A168030.
%K A168148 nonn
%O A168148 0,3
%A A168148 _Philippe Deléham_, Nov 19 2009
%E A168148 Terms a(16) onward added by _G. C. Greubel_, Jan 12 2023