|
| |
|
|
A190412
|
|
Decimal expansion of sum over upper triangular subarray of array G defined at A190404.
|
|
3
|
|
|
|
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, 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, 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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
See A190404.
|
|
|
LINKS
|
Danny Rorabaugh, Table of n, a(n) for n = 0..500
|
|
|
EXAMPLE
|
0.85635039560977957398146182399142454489929399971437975...
|
|
|
MATHEMATICA
|
f[i_, j_] := i + (j + i - 2)(j + i - 1)/2; (* natural number array, A000027 *)
g[i_, j_] := (1/2)^f[i, j];
d[h_] := Sum[g[i, i+h-1], {i, 1, 250}]; (* h-th up-diag sum *)
e[h_] := Sum[g[i+h, i], {i, 1, 250}]; (* h-th low-diag sum *)
c1 = N[Sum[d[j], {j, 1, 30}], 50]
RealDigits[c1, 10, 50, -1] (* A190412 *)
c2 = N[Sum[e[i], {i, 1, 30}], 50]
RealDigits[c2, 10, 50, -1] (* A190415 *)
c1 + c2 (* very close to 1 *)
|
|
|
PROG
|
(Sage)
def A190412(b): # Generate the constant with b bits of precision
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)
A190412(365) # Danny Rorabaugh, Mar 26 2015
|
|
|
CROSSREFS
|
Cf. A190404, A190415.
Sequence in context: A335339 A107828 A256155 * A199615 A199059 A065415
Adjacent sequences: A190409 A190410 A190411 * A190413 A190414 A190415
|
|
|
KEYWORD
|
nonn,cons
|
|
|
AUTHOR
|
Clark Kimberling, May 10 2011
|
|
|
EXTENSIONS
|
a(49) corrected and a(50)-a(105) added by Danny Rorabaugh, Mar 24 2015
|
|
|
STATUS
|
approved
|
| |
|
|
