Template:Sequence of the Day for February 4

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

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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.