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A190411 Decimal expansion of sum of even-numbered columns of array G defined at A190404.

%I A190411 #11 Mar 26 2015 11:45:55
%S A190411 2,9,1,3,4,0,9,8,6,8,8,2,7,6,3,2,8,4,6,3,0,3,5,1,4,0,7,9,4,7,3,2,3,6,
%T A190411 6,6,7,9,8,4,0,3,0,5,8,6,7,9,5,9,4,9,0,2,7,1,1,2,9,5,6,2,6,7,8,5,6,5,
%U A190411 3,5,6,4,8,3,1,5,2,5,2,6,4,0,0,1,1,0,3,3,2,1,0,5,5,5,7,5,6,0,1,9,3,2,5,2,9,6,7,9,9,0,7,9,6,5,9,0
%N A190411 Decimal expansion of sum of even-numbered columns of array G defined at A190404.
%C A190411 See A190404.
%H A190411 Danny Rorabaugh, <a href="/A190411/b190411.txt">Table of n, a(n) for n = 0..500</a>
%e A190411 0.29134098688276328463035140794732366679840305867959490...
%t A190411 f[i_, j_] :=  i + (j + i - 2)(j + i - 1)/2; (* natural number array, A000027 *)
%t A190411 g[i_, j_] := (1/2)^f[i, j];
%t A190411 c[j_] := Sum[g[i,j], {i,1,400}]; (* j-th column sum of G *)
%t A190411 c1 = N[Sum[c[2 i - 1], {i, 1, 10}], 60]
%t A190411 RealDigits[c1, 10, 60, -1]  (* A190410 *)
%t A190411 c2 = N[Sum[c[2 i], {i, 1, 10}], 60]
%t A190411 RealDigits[c2, 10, 60, -1]  (* A190411 *)
%t A190411 c1 + c2 (* very close to 1 *)
%o A190411 def A190411(b): # Generate the constant with b bits of precision
%o A190411 ..return N(sum([sum([(1/2)^(i+(j+i-2)*(j+i-1)/2) for i in range(1,b)]) for j in range(2,b,2)]),b)
%o A190411 A190411(390) # _Danny Rorabaugh_, Mar 26 2015
%Y A190411 Cf. A190404, A190410.
%K A190411 nonn,cons
%O A190411 0,1
%A A190411 _Clark Kimberling_, May 10 2011
%E A190411 a(69)-a(79) corrected and a(80)-a(115) added by _Danny Rorabaugh_, Mar 26 2015