A190409 Decimal expansion of sum of even-numbered rows of array G defined at A190404.

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

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

Cf. A190404, A190408.

Sequence in context: A082344 A021865 A198565 * A068226 A011237 A195433

Adjacent sequences: A190406 A190407 A190408 * A190410 A190411 A190412

Keyword

nonn,cons

Author

Clark Kimberling, May 10 2011

Extensions

a(75)-a(103) corrected by Danny Rorabaugh, Mar 24 2015

Status

approved