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A190408 Decimal expansion of sum of odd-numbered rows of array G defined at A190404.

%I A190408 #17 Mar 16 2020 09:29:33
%S A190408 8,3,8,5,5,1,8,4,0,4,3,4,4,8,1,2,4,0,0,6,1,6,3,2,3,3,1,3,5,5,8,0,0,1,
%T A190408 4,4,8,7,3,7,5,6,9,0,4,6,6,5,1,7,4,8,1,8,6,4,6,1,7,9,5,0,0,9,1,2,3,6,
%U A190408 8,4,3,2,7,4,2,6,4,2,5,2,2,5,3,4,5,5,8,0,4,4,9,3,0,0,2,8,6,4,6,2,9,4,5,5,9,5,9,1,6,8,0,0,8,0,4,4,2,3,6,0
%N A190408 Decimal expansion of sum of odd-numbered rows of array G defined at A190404.
%C A190408 See A190404.
%H A190408 Danny Rorabaugh, <a href="/A190408/b190408.txt">Table of n, a(n) for n = 0..500</a>
%e A190408 0.8385518404344812400616323313558001448737569046651...
%t A190408 f[i_, j_] :=  i + (j + i - 2)(j + i - 1)/2; (* natural number array, A000027 *)
%t A190408 g[i_, j_] := (1/2)^f[i, j]; (* array G *)
%t A190408 r[i_] := Sum[g[i,j], {j,1,400}];  (* i-th row sum of G *)
%t A190408 c1 = N[Sum[r[2 i - 1], {i, 1, 10}], 60]
%t A190408 RealDigits[c1, 10, 60, -1] (* A190408 *)
%t A190408 c2 = N[Sum[r[2 i], {i, 1, 10}], 60]
%t A190408 RealDigits[c2, 10, 60, -1] (* A190409 *)
%t A190408 c1 + c2 (* very close to 1 *)
%o A190408 (Sage)
%o A190408 def A190408(b): # Generate the constant with b bits of precision
%o A190408     return N(sum([sum([(1/2)^(i+(j+i-2)*(j+i-1)/2) for j in range(1,b)]) for i in range(1,b,2)]),b)
%o A190408 A190408(405) # _Danny Rorabaugh_, Mar 26 2015
%Y A190408 Cf. A190404, A190409.
%K A190408 nonn,cons
%O A190408 0,1
%A A190408 _Clark Kimberling_, May 10 2011
%E A190408 a(69)-a(119) corrected by _Danny Rorabaugh_, Mar 26 2015