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

Author

Clark Kimberling, May 10 2011

Keywords

• nonn
• cons

Comments

See A190404.

Examples

			0.85635039560977957398146182399142454489929399971437975...
		

Links

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

Crossrefs

Cf. A190404, A190415.

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 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

Extensions

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