A190412 Decimal expansion of sum over upper triangular subarray of array G defined at A190404.

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

Offset

0,1

Comments

See A190404.

Links

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

Example

0.85635039560977957398146182399142454489929399971437975...

Mathematica

f[i_, j_] :=  i + (j + i - 2)(j + i - 1)/2; (* natural number array, A000027 *)
g[i_, j_] := (1/2)^f[i, j];
d[h_] := Sum[g[i, i+h-1], {i, 1, 250}]; (* h-th up-diag sum *)
e[h_] := Sum[g[i+h, i], {i, 1, 250}];   (* h-th low-diag sum *)
c1 = N[Sum[d[j], {j, 1, 30}], 50]
RealDigits[c1, 10, 50, -1]  (* A190412 *)
c2 = N[Sum[e[i], {i, 1, 30}], 50]
RealDigits[c2, 10, 50, -1] (* A190415 *)
c1 + c2 (* very close to 1 *)

Prog

(Sage)
def A190412(b): # Generate the constant with b bits of precision
    return N(sum([sum([(1/2)^(i+(j+2*i-3)*(j+2*i-2)/2) for i in range(1, b)]) for j in range(1, b)]), b)
A190412(365) # Danny Rorabaugh, Mar 26 2015

Crossrefs

Cf. A190404, A190415.

Sequence in context: A335339 A107828 A256155 * A199615 A199059 A065415

Adjacent sequences: A190409 A190410 A190411 * A190413 A190414 A190415

Keyword

nonn,cons

Author

Clark Kimberling, May 10 2011

Extensions

a(49) corrected and a(50)-a(105) added by Danny Rorabaugh, Mar 24 2015

Status

approved