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A291196 Third differences of {Pi*n^2}, fractional part of Pi*n^2. 1
1, 0, -1, 2, -3, 3, -2, 1, 0, 0, -1, 1, -1, 2, -2, 0, 2, -2, 1, 0, -1, 1, 0, -1, 1, 0, 0, -1, 2, -3, 3, -2, 1, 0, -1, 1, 0, -1, 2, -2, 0, 2, -2, 1, -1, 2, -2, 0, 2, -2, 1, -1, 1, 0, 0, 0, -1, 1, -1, 2, -2, 0, 2, -2, 1, -1, 2, -2, 0, 2, -2, 1, 0, -1, 1, 0, -1, 2, -3, 3, -2, 1, 0, 0, -1, 1, 0, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

From Robert Israel, Aug 20 2017: (Start)

-3 <= a(n) <= 3.

It appears that:

   a(n) = -3 if and only if a(n+1) = 3.

   if a(n) = -2 then a(n+1) = 0, 1 or 2.

   if a(n) = -1 or 0 then a(n+1) = -1, 0, 1 or 2.

   if a(n) = 1 then a(n+1) = -3, -1, 0 or 1.

   if a(n) = 2 then a(n+1) = -3 or -2.

   if a(n) = 3 then a(n+1) = -2 or -1.

(End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = {Pi*(n+3)^2} - 3*{Pi*(n+2)^2) + 3*{Pi*(n+1)^2} - {Pi*n^2}.

MAPLE

A0:= [seq(frac(Pi*n^2), n=1..103)]:

A1:= A0[2..-1]-A0[1..-2]:

A2:= A1[2..-1]-A1[1..-2]:

A2[2..-1]-A2[1..-2]; # Robert Israel, Aug 20 2017

CROSSREFS

Sequence in context: A101914 A099530 A167544 * A279316 A074989 A307429

Adjacent sequences:  A291193 A291194 A291195 * A291197 A291198 A291199

KEYWORD

sign

AUTHOR

Simon Plouffe, Aug 20 2017

STATUS

approved

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Last modified October 18 04:54 EDT 2019. Contains 328145 sequences. (Running on oeis4.)