A190411 Decimal expansion of sum of even-numbered columns of array G defined at A190404.

2, 9, 1, 3, 4, 0, 9, 8, 6, 8, 8, 2, 7, 6, 3, 2, 8, 4, 6, 3, 0, 3, 5, 1, 4, 0, 7, 9, 4, 7, 3, 2, 3, 6, 6, 6, 7, 9, 8, 4, 0, 3, 0, 5, 8, 6, 7, 9, 5, 9, 4, 9, 0, 2, 7, 1, 1, 2, 9, 5, 6, 2, 6, 7, 8, 5, 6, 5, 3, 5, 6, 4, 8, 3, 1, 5, 2, 5, 2, 6, 4, 0, 0, 1, 1, 0, 3, 3, 2, 1, 0, 5, 5, 5, 7, 5, 6, 0, 1, 9, 3, 2, 5, 2, 9, 6, 7, 9, 9, 0, 7, 9, 6, 5, 9, 0

Offset

0,1

Comments

See A190404.

Links

Danny Rorabaugh, Table of n, a(n) for n = 0..500

Example

0.29134098688276328463035140794732366679840305867959490...

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

def A190411(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(2, b, 2)]), b)
A190411(390) # Danny Rorabaugh, Mar 26 2015

Crossrefs

Cf. A190404, A190410.

Sequence in context: A011064 A086773 A176124 * A190142 A173995 A272868

Adjacent sequences: A190408 A190409 A190410 * A190412 A190413 A190414

Keyword

nonn,cons

Author

Clark Kimberling, May 10 2011

Extensions

a(69)-a(79) corrected and a(80)-a(115) added by Danny Rorabaugh, Mar 26 2015

Status

approved