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A190412 Decimal expansion of sum over upper triangular subarray of array G defined at A190404. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A154433 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

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Last modified May 22 06:32 EDT 2019. Contains 323478 sequences. (Running on oeis4.)