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A190415 Decimal expansion of sum over lower triangular subarray of array G defined at A190404. 3
1, 4, 3, 6, 4, 9, 6, 0, 4, 3, 9, 0, 2, 2, 0, 4, 2, 6, 0, 1, 8, 5, 3, 8, 1, 7, 6, 0, 0, 8, 5, 7, 5, 4, 5, 5, 1, 0, 0, 7, 0, 6, 0, 0, 0, 2, 8, 5, 6, 2, 0, 2, 4, 6, 7, 3, 7, 2, 4, 7, 8, 9, 5, 9, 6, 2, 7, 6, 5, 9, 2, 9, 8, 1, 4, 9, 7, 0, 4, 2, 2, 7, 7, 1, 2, 6, 9, 5, 6, 2, 8, 1, 8, 9, 0, 4, 3, 8, 8, 1, 1, 2, 8, 0, 7, 2, 6, 7, 8, 7, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See A190404.

LINKS

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

EXAMPLE

0.14364960439022042601853817600857545510070600028562...

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 A190415(b): # Generate the constant with b bits of precision

return N(sum([sum([(1/2)^(i+j+(j+2*i-2)*(j+2*i-1)/2) for i in range(1, b)]) for j in range(1, b)]), b)

A190415(379) # Danny Rorabaugh, Mar 26 2015

CROSSREFS

Cf. A190404, A190412.

Sequence in context: A290278 A300894 A328258 * A024602 A131603 A242554

Adjacent sequences: A190412 A190413 A190414 * A190416 A190417 A190418

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, May 10 2011

EXTENSIONS

a(50)-a(111) from Danny Rorabaugh, Mar 26 2015

STATUS

approved

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Last modified February 3 08:31 EST 2023. Contains 360034 sequences. (Running on oeis4.)