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A228049 Decimal expansion of sum of reciprocals, column 3 of the natural number array, A185787. 6
7, 9, 8, 4, 1, 0, 5, 5, 1, 0, 1, 6, 8, 7, 8, 0, 0, 3, 8, 6, 5, 2, 6, 6, 5, 1, 7, 5, 6, 1, 3, 2, 6, 5, 8, 1, 6, 6, 2, 7, 9, 3, 1, 6, 1, 9, 5, 4, 9, 8, 8, 5, 5, 7, 4, 1, 5, 2, 8, 6, 8, 7, 1, 8, 1, 1, 5, 7, 7, 8, 3, 0, 9, 5, 1, 4, 3, 1, 1, 1, 3, 3, 5, 4, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let s(n) be the sum of reciprocals of the numbers in row n of the array T at A185787 given by T(n,k) = n + (n+k-2)(n+k-1)/2, and let r = (2*pi/sqrt(7))*tanh(pi*sqrt(7)/2), as at A226985. Then s(1) = r, and s(2) to s(5) are given by A228044 to A228047.

Let c(n) be the sum of reciprocals of the numbers in column n of T.  Then c(1) = 2; c(2) = 11/9, c(4) = 29/50, and c(3) is given by A228049.  Let d(n) be the sum of reciprocals of the numbers in the main diagonal, (T(n,n)); then d(2) = (1/12)*(pi)^2; d(3) = 1/2, and d(1) is given by A228048.

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

1/4 + 1/8 + 1/13 + ... = (1/34)(17 + 8r*tan(r)), where r = (pi/2)sqrt(17)

1/4 + 1/8 + 1/13 + ... = 0.79841055101687800386526651756132658166...

MATHEMATICA

$MaxExtraPrecision = Infinity; t[n_, k_] := t[n, k] = n + (n + k - 2) (n + k - 1)/2; u = N[Sum[1/t[n, 3], {n, 1, Infinity}], 130]; RealDigits[u, 10]

CROSSREFS

Cf. A185787, A000027, A228044, A226985.

Sequence in context: A256924 A259069 A209328 * A154943 A126041 A319881

Adjacent sequences:  A228046 A228047 A228048 * A228050 A228051 A228052

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Aug 06 2013

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)