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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188645 Array of ((k^n)+(k^(-n)))/2 where k=((x^2+1)^(1/2)+x)^2 for integers x>=1 13
1, 3, 1, 17, 9, 1, 99, 161, 19, 1, 577, 2889, 721, 33, 1, 3363, 51841, 27379, 2177, 51, 1, 19601, 930249, 1039681, 143649, 5201, 73, 1, 114243, 16692641, 39480499, 9478657, 530451, 10657, 99, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Conjecture by C Hohn: Given function f(x, y)=((x^2+y)^(1/2)+x)^2; and constant k=f(x, y); then for all integers x>=1 and y=[+-]1, k may be irrational, but ((k^n)+(k^(-n)))/2 always produces integer sequences; y=1 results shown here; y=-1 results are A188644

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(n)=(A188647(n-1)+A188647(n))/2

EXAMPLE

1, 3, 17, 99, 577, 3363, 19601, 114243, ...

1, 9, 161, 2889, 51841, 930249, 16692641, ...

1, 19, 721, 27379, 1039681, 39480499, ...

1, 33, 2177, 143649, 9478657, 625447713, ...

1, 51, 5201, 530451, 54100801, ...

1, 73, 10657, 1555849, 227143297, ...

1, 99, 19601, 3880899, 768398401, ...

1, 129, 33281, 8586369, 2215249921, ...

1, 163, 53137, 17322499, 5647081537, ...

1, 201, 80801, 32481801, 13057603201, ...

1, 243, 118097, 57394899, 27893802817, ...

1, 289, 167041, 96549409, 55805391361, ...

1, 339, 229841, 155831859, 105653770561, ...

1, 393, 308897, 242792649, 190834713217, ...

1, 451, 406801, 366934051, 330974107201, ...

...

MATHEMATICA

max = 9; y = 1; t = Table[k = ((x^2 + y)^(1/2) + x)^2; ((k^n) + (k^(-n)))/2 // FullSimplify, {n, 0, max - 1}, {x, 1, max}]; Table[ t[[n - k + 1, k]], {n, 1, max}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Jul 17 2013 *)

CROSSREFS

Row 1 is A001541, row 2 is A023039, row 3 is A078986, row 4 is A099370, row 5 is A099397, row 6 is A174747, row 8 is A176368, (row 1)*2 is A003499, (row 2)*2 is A087215.

Column 2 is A058331, (column 2)*2 is A005899.

A188644 (f(x, y) as above with y=-1).

Sequence in context: A259031 A259686 A162313 * A060281 A151918 A089974

Adjacent sequences:  A188642 A188643 A188644 * A188646 A188647 A188648

KEYWORD

nonn,tabl

AUTHOR

Charles L. Hohn, Apr 06 2011

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 21:23 EST 2018. Contains 299588 sequences. (Running on oeis4.)