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Template:Sequence of the Day for February 4

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Intended for: February 4, 2013

Timetable

  • First draft entered by Alonso del Arte on November 3, 2011
  • Draft reviewed by Alonso del Arte on December 1, 2012
  • Draft to be approved by January 4, 2012

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A116697:
a (0) = 1; a (1) = 1; a (2) =  −  2; a (3) = 2; a (n) =  −  a (n  −  1)  −  a (n  −  3) + a (n  −  4), n   ≥   4
.
{ 1, 1, −2, 2, −2, 5, − 9, 13, −20, ... }
This a homogeneous linear recurrence (of order 4) with constant coefficients. Most recurrence relations use the last few consecutive terms (usually two) to determine the next term. But in this one,
a (n  −  2)
is actually ignored, and
a (n  −  3)
and
a (n  −  4)
are used. There’s something else that is interesting about this sequence: read the odd-indexed terms and see if that reminds you of anything.