A190408 Decimal expansion of sum of odd-numbered rows of array G defined at A190404.

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

Offset

0,1

Comments

See A190404.

Links

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

Example

0.8385518404344812400616323313558001448737569046651...

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 A190408(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(1, b, 2)]), b)
A190408(405) # Danny Rorabaugh, Mar 26 2015

Crossrefs

Cf. A190404, A190409.

Sequence in context: A199598 A011106 A131641 * A343851 A085672 A019866

Adjacent sequences: A190405 A190406 A190407 * A190409 A190410 A190411

Keyword

nonn,cons

Author

Clark Kimberling, May 10 2011

Extensions

a(69)-a(119) corrected by Danny Rorabaugh, Mar 26 2015

Status

approved