A190410 Decimal expansion of sum of odd-numbered columns of array G defined at A190404.

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

Offset

0,1

Comments

See A190404.

Links

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

Example

0.708659013117236715369648592052676333201596941320...

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

(Sage)
def A190410(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(1, b, 2)]), b)
A190410(350) # Danny Rorabaugh, Mar 24 2015

Crossrefs

Cf. A190404, A190411.

Sequence in context: A322910 A198939 A290372 * A283881 A178308 A320377

Adjacent sequences: A190407 A190408 A190409 * A190411 A190412 A190413

Keyword

nonn,cons

Author

Clark Kimberling, May 10 2011

Extensions

a(62)-a(79) corrected and a(80)-a(103) added by Danny Rorabaugh, Mar 24 2015

Status

approved