A190415 Decimal expansion of sum over lower triangular subarray of array G defined at A190404.

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

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 A367269 A131603

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