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

Author

Clark Kimberling, May 10 2011

Keywords

• nonn
• cons

Comments

See A190404.

Examples

			0.708659013117236715369648592052676333201596941320...
		

Links

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

Crossrefs

Cf. A190404, A190411.

Programs

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 *)

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

Extensions

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