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%I #18 Mar 16 2020 09:29:52
%S 8,5,6,3,5,0,3,9,5,6,0,9,7,7,9,5,7,3,9,8,1,4,6,1,8,2,3,9,9,1,4,2,4,5,
%T 4,4,8,9,9,2,9,3,9,9,9,7,1,4,3,7,9,7,5,3,2,6,2,7,5,2,1,0,4,0,3,7,2,3,
%U 4,0,7,0,1,8,5,0,2,9,5,7,7,2,2,8,7,3,0,4,3,7,1,8,1,0,9,5,6,1,1,8,8,7,1,9,2,7
%N Decimal expansion of sum over upper triangular subarray of array G defined at A190404.
%C See A190404.
%H Danny Rorabaugh, <a href="/A190412/b190412.txt">Table of n, a(n) for n = 0..500</a>
%e 0.85635039560977957398146182399142454489929399971437975...
%t f[i_, j_] := i + (j + i - 2)(j + i - 1)/2; (* natural number array, A000027 *)
%t g[i_, j_] := (1/2)^f[i, j];
%t d[h_] := Sum[g[i,i+h-1], {i,1,250}]; (* h-th up-diag sum *)
%t e[h_] := Sum[g[i+h,i], {i,1,250}]; (* h-th low-diag sum *)
%t c1 = N[Sum[d[j], {j, 1, 30}], 50]
%t RealDigits[c1, 10, 50, -1] (* A190412 *)
%t c2 = N[Sum[e[i], {i, 1, 30}], 50]
%t RealDigits[c2, 10, 50, -1] (* A190415 *)
%t c1 + c2 (* very close to 1 *)
%o (Sage)
%o def A190412(b): # Generate the constant with b bits of precision
%o return N(sum([sum([(1/2)^(i+(j+2*i-3)*(j+2*i-2)/2) for i in range(1,b)]) for j in range(1,b)]),b)
%o A190412(365) # _Danny Rorabaugh_, Mar 26 2015
%Y Cf. A190404, A190415.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, May 10 2011
%E a(49) corrected and a(50)-a(105) added by _Danny Rorabaugh_, Mar 24 2015
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