login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A262396 Product of the sums and differences of the square roots of the first n positive integers, combined in all possible ways. 1
1, -1, 1, 64, 4096, 23323703841, 63703464216016403230349121, 316699666163357097153212433469030615484754548657341071360000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The series increases rapidly and the next number in the sequence has 135 decimal digits. Each element for n>1 is necessarily both an integer and a perfect square, the square roots being 1, 8, 64, 152721, 7981444995489, 562760753929551396141111705600, ...

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10

EXAMPLE

a(0) = 1 = (empty product).

a(1) = -1 = (sqrt(1)) * (-sqrt(1)).

a(2) = 1 = (1+sqrt(2)) * (1-sqrt(2)) * (-1+sqrt(2)) * (-1-sqrt(2)).

a(3) = 64 = (1+sqrt(2)+sqrt(3)) * (1+sqrt(2)-sqrt(3)) * (1-sqrt(2)+sqrt(3)) * (1-sqrt(2)-sqrt(3)) * (-1+sqrt(2)+sqrt(3)) * (-1+sqrt(2)-sqrt(3)) * (-1-sqrt(2)+sqrt(3)) * (-1-sqrt(2)-sqrt(3)).

MAPLE

s:= proc(n) option remember; `if`(n<2, [1, -1][1..2*n],

       map(x-> [x+sqrt(n), x-sqrt(n)][], s(n-1)))

    end:

a:= n-> expand(mul(t, t=s(n))):

seq(a(n), n=0..7);  # Alois P. Heinz, Sep 21 2015

CROSSREFS

Sequence in context: A144320 A324493 A324490 * A318015 A320401 A203438

Adjacent sequences:  A262393 A262394 A262395 * A262397 A262398 A262399

KEYWORD

sign

AUTHOR

Mark Bradley, Sep 21 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)