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A190410 Decimal expansion of sum of odd-numbered columns of array G defined at A190404.

%I A190410 #17 Mar 16 2020 09:29:47
%S A190410 7,0,8,6,5,9,0,1,3,1,1,7,2,3,6,7,1,5,3,6,9,6,4,8,5,9,2,0,5,2,6,7,6,3,
%T A190410 3,3,2,0,1,5,9,6,9,4,1,3,2,0,4,0,5,0,9,7,2,8,8,7,0,4,3,7,3,2,1,4,3,4,
%U A190410 6,4,3,5,1,6,8,4,7,4,7,3,5,9,9,8,8,9,6,6,7,8,9,4,4,4,2,4,3,9,8,0,6,7,4,7
%N A190410 Decimal expansion of sum of odd-numbered columns of array G defined at A190404.
%C A190410 See A190404.
%H A190410 Danny Rorabaugh, <a href="/A190410/b190410.txt">Table of n, a(n) for n = 0..500</a>
%e A190410 0.708659013117236715369648592052676333201596941320...
%t A190410 f[i_, j_] :=  i + (j + i - 2) (j + i - 1)/2; (* natural number array, A000027 *)
%t A190410 g[i_, j_] := (1/2)^f[i, j];
%t A190410 c[j_] := Sum[g[i,j], {i,1,400}]; (* j-th column sum of G *)
%t A190410 c1 = N[Sum[c[2 i - 1], {i, 1, 10}], 60]
%t A190410 RealDigits[c1, 10, 60, -1]  (* A190410 *)
%t A190410 c2 = N[Sum[c[2 i], {i, 1, 10}], 60]
%t A190410 RealDigits[c2, 10, 60, -1]  (* A190411 *)
%t A190410 c1 + c2 (* very close to 1 *)
%o A190410 (Sage)
%o A190410 def A190410(b): # Generate the constant with b bits of precision
%o A190410     return N(sum([sum([(1/2)^(i+(j+i-2)*(j+i-1)/2) for i in range(1,b)]) for j in range(1,b,2)]),b)
%o A190410 A190410(350) # _Danny Rorabaugh_, Mar 24 2015
%Y A190410 Cf. A190404, A190411.
%K A190410 nonn,cons
%O A190410 0,1
%A A190410 _Clark Kimberling_, May 10 2011
%E A190410 a(62)-a(79) corrected and a(80)-a(103) added by _Danny Rorabaugh_, Mar 24 2015