A190409 - OEIS

%I #16 Mar 16 2020 09:29:41

%S 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,

%T 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,

%U 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

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

%C See A190404.

%H Danny Rorabaugh, <a href="/A190409/b190409.txt">Table of n, a(n) for n = 0..500</a>

%e 0.161448159565518759938367668644199855126243095334825...

%t f[i_, j_] :=  i + (j + i - 2) (j + i - 1)/2; (* natural number array, A000027 *)

%t g[i_,j_] := (1/2)^f[i, j]; (* array G *)

%t r[i_] := Sum[g[i, j], {j,1,400}]; (* i-th row sum of G *)

%t c1 = N[Sum[r[2 i - 1], {i, 1, 10}], 60]

%t RealDigits[c1, 10, 60, -1] (* A190408 *)

%t c2 = N[Sum[r[2 i], {i, 1, 10}], 60]

%t RealDigits[c2, 10, 60, -1] (* A190409 *)

%t c1 + c2 (* very close to 1 *)

%o (Sage)

%o def A190409(b): # Generate the constant with b bits of precision

%o     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)

%o A190409(350) # _Danny Rorabaugh_, Mar 25 2015

%Y Cf. A190404, A190408.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, May 10 2011

%E a(75)-a(103) corrected by _Danny Rorabaugh_, Mar 24 2015