A328495 Decimal expansion of Sum_{k>=0} (-1)^k*L(k)/k!, where L(k) is the k-th Lucas number (A000032).

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

Offset

1,1

References

Thomas Koshy, Fibonacci and Lucas Numbers with Applications, Volume 1, 2nd edition, Wiley, 2017, chapter 13.8, pp. 248-250.

Links

Table of n, a(n) for n=1..87.

Formula

Equals exp(-phi) + exp(phi-1), where phi is the golden ratio (A001622).

Equals 2*exp(-1/2)*cosh(sqrt(5)/2) = A249455*cosh(phi - 1/2). - Peter Luschny, Oct 22 2019

Equals A328344 / e. - Amiram Eldar, Feb 06 2022

Example

2.053565111476510960344914661146965309320258644945918...

Maple

Digits := 100: 2*exp(-1/2)*cosh(sqrt(5)/2)*10^86:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Oct 22 2019

Mathematica

RealDigits[Exp[-GoldenRatio] + Exp[GoldenRatio - 1], 10, 100][[1]]

Crossrefs

Cf. A000032, A001113, A001622, A099935, A139341, A139342, A328344, A249455.

Sequence in context: A324654 A121705 A071782 * A297024 A356215 A107363

Adjacent sequences: A328492 A328493 A328494 * A328496 A328497 A328498

Keyword

nonn,cons

Author

Amiram Eldar, Oct 22 2019

Status

approved