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A190409 Decimal expansion of sum of even-numbered rows of array G defined at A190404.

%I A190409 #16 Mar 16 2020 09:29:41
%S A190409 1,6,1,4,4,8,1,5,9,5,6,5,5,1,8,7,5,9,9,3,8,3,6,7,6,6,8,6,4,4,1,9,9,8,
%T A190409 5,5,1,2,6,2,4,3,0,9,5,3,3,4,8,2,5,1,8,1,3,5,3,8,2,0,4,9,9,0,8,7,6,3,
%U A190409 1,5,6,7,2,5,7,3,5,7,4,7,7,4,6,5,4,4,1,9,5,5,0,6,9,9,7,1,3,5,3,7,0,5,4,4
%N A190409 Decimal expansion of sum of even-numbered rows of array G defined at A190404.
%C A190409 See A190404.
%H A190409 Danny Rorabaugh, <a href="/A190409/b190409.txt">Table of n, a(n) for n = 0..500</a>
%e A190409 0.161448159565518759938367668644199855126243095334825...
%t A190409 f[i_, j_] :=  i + (j + i - 2) (j + i - 1)/2; (* natural number array, A000027 *)
%t A190409 g[i_,j_] := (1/2)^f[i, j]; (* array G *)
%t A190409 r[i_] := Sum[g[i, j], {j,1,400}]; (* i-th row sum of G *)
%t A190409 c1 = N[Sum[r[2 i - 1], {i, 1, 10}], 60]
%t A190409 RealDigits[c1, 10, 60, -1] (* A190408 *)
%t A190409 c2 = N[Sum[r[2 i], {i, 1, 10}], 60]
%t A190409 RealDigits[c2, 10, 60, -1] (* A190409 *)
%t A190409 c1 + c2 (* very close to 1 *)
%o A190409 (Sage)
%o A190409 def A190409(b): # Generate the constant with b bits of precision
%o A190409     return N(sum([sum([(1/2)^(i+(j+i-2)*(j+i-1)/2) for j in range(1,b)]) for i in range(2,b,2)]),b)
%o A190409 A190409(350) # _Danny Rorabaugh_, Mar 25 2015
%Y A190409 Cf. A190404, A190408.
%K A190409 nonn,cons
%O A190409 0,2
%A A190409 _Clark Kimberling_, May 10 2011
%E A190409 a(75)-a(103) corrected by _Danny Rorabaugh_, Mar 24 2015