OFFSET
0,2
COMMENTS
See A190404.
LINKS
Danny Rorabaugh, Table of n, a(n) for n = 0..500
EXAMPLE
0.161448159565518759938367668644199855126243095334825...
MATHEMATICA
f[i_, j_] := i + (j + i - 2) (j + i - 1)/2; (* natural number array, A000027 *)
g[i_, j_] := (1/2)^f[i, j]; (* array G *)
r[i_] := Sum[g[i, j], {j, 1, 400}]; (* i-th row sum of G *)
c1 = N[Sum[r[2 i - 1], {i, 1, 10}], 60]
RealDigits[c1, 10, 60, -1] (* A190408 *)
c2 = N[Sum[r[2 i], {i, 1, 10}], 60]
RealDigits[c2, 10, 60, -1] (* A190409 *)
c1 + c2 (* very close to 1 *)
PROG
(Sage)
def A190409(b): # Generate the constant with b bits of precision
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)
A190409(350) # Danny Rorabaugh, Mar 25 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 10 2011
EXTENSIONS
a(75)-a(103) corrected by Danny Rorabaugh, Mar 24 2015
STATUS
approved