OFFSET
0,1
COMMENTS
See A190404.
LINKS
Danny Rorabaugh, Table of n, a(n) for n = 0..500
EXAMPLE
0.708659013117236715369648592052676333201596941320...
MATHEMATICA
f[i_, j_] := i + (j + i - 2) (j + i - 1)/2; (* natural number array, A000027 *)
g[i_, j_] := (1/2)^f[i, j];
c[j_] := Sum[g[i, j], {i, 1, 400}]; (* j-th column sum of G *)
c1 = N[Sum[c[2 i - 1], {i, 1, 10}], 60]
RealDigits[c1, 10, 60, -1] (* A190410 *)
c2 = N[Sum[c[2 i], {i, 1, 10}], 60]
RealDigits[c2, 10, 60, -1] (* A190411 *)
c1 + c2 (* very close to 1 *)
PROG
(Sage)
def A190410(b): # Generate the constant with b bits of precision
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)
A190410(350) # Danny Rorabaugh, Mar 24 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 10 2011
EXTENSIONS
a(62)-a(79) corrected and a(80)-a(103) added by Danny Rorabaugh, Mar 24 2015
STATUS
approved