A324007 Decimal expansion of the sum of reciprocals of the products of 3 consecutive Fibonacci numbers.

7, 1, 0, 8, 5, 5, 3, 5, 1, 4, 2, 9, 3, 2, 8, 4, 1, 6, 8, 8, 7, 6, 9, 4, 4, 9, 0, 3, 8, 4, 2, 7, 0, 8, 3, 3, 0, 4, 5, 1, 1, 8, 0, 4, 8, 4, 1, 0, 3, 0, 8, 6, 3, 9, 9, 7, 4, 9, 7, 3, 5, 1, 4, 9, 3, 6, 9, 6, 4, 2, 3, 8, 2, 6, 1, 1, 3, 5, 4, 4, 8, 4, 1, 7, 5, 8, 8, 4, 1, 6, 8, 1, 7, 1, 4, 8, 5, 8, 5, 7, 6, 8, 5, 4, 9

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Brother Alfred Brousseau, Summation of Infinite Fibonacci Series, The Fibonacci Quarterly, Vol. 7, No. 2 (1969), pp. 143-168.

R. S. Melham, On Some Reciprocal Sums of Brousseau: An Alternative Approach to That of Carlitz, Fibonacci Quarterly, Vol. 41, No. 1 (2003), pp. 59-62.

Formula

From Amiram Eldar, Feb 09 2023: (Start)

Equals Sum_{k>=1} 1/A065563(k).

Equals 1 - A158933 (Melham, 2003). (End)

Example

0.71085535142932841688769449038427083304511804841030863997497351493696423826...

Mathematica

RealDigits[ Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k + 2}], 128], {k, 177}], 10, 111][[1]]

Prog

(PARI) suminf(n=1, 1/(fibonacci(n)*fibonacci(n+1)*fibonacci(n+2))) \\ Michel Marcus, Feb 19 2019

Crossrefs

Cf. A000045, A065563, A079586, A158933, A290565, A322711, A324008.

Sequence in context: A198212 A217245 A154098 * A176442 A361602 A281115

Adjacent sequences: A324004 A324005 A324006 * A324008 A324009 A324010

Keyword

nonn,cons

Author

Robert G. Wilson v, Feb 11 2019

Status

approved