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

Author

Clark Kimberling, May 10 2011

Keywords

• nonn
• cons

Comments

See A190404.

Examples

			0.14364960439022042601853817600857545510070600028562...
		

Links

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

Crossrefs

Cf. A190404, A190412.

Programs

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 *)

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

Extensions

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