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

Author

Clark Kimberling, May 10 2011

Keywords

• nonn
• cons

Comments

See A190404.

Examples

			0.161448159565518759938367668644199855126243095334825...
		

Links

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

Crossrefs

Cf. A190404, A190408.

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]; (* 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 *)

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

Extensions

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