[seqfan] Some items inspired by appearances of 2009 in the OEIS

[Marc LeBrun]

Some items inspired by appearances of 2009 in the OEIS.  "Enjoy"!


Miscellany:

A009720:  2009 is the 7th derivative of tan(tanh(x)*cos(x)) at x=0

A046735:  2009 does not divide any Tribonacci number

A051336:  There are 2009 arithmetic progressions in {1,2,3,...,35}

A067593:  There are 2009 partitions of 39 into Lucas numbers


Possible Puzzles:

A025405, A025409 etc:
Trivial partitioning of 2009 into 4 cubes: 1^3 + 2^3 + 10^3 + 10^3
Knowing the Ramanujan-Hardy taxicab story, do it in two distinctly 
different ways.

A056745:  Show 2009 divides 6^2009 + 5^2009 + 4^2009 + 3^2009 + 
2^2009 + 1^2009 [over 3K digits]


Mysterious(?) Coincidences:

A006768:  There are 2009 5-dimensional polyominoes with 8 cells
A057865:  There are 2009 simple Hamilton-connected graphs on 8 nodes
[And Mathworld says, "...every 8-connected claw-free graph is 
Hamilton-connected (Hu et al. 2005)"].

A008764:  There are 2009 nonisomorphic symmetric 3 X 3 matrices over 
Z with row and column sums equal to 49   [Note that 49 divides 2009; 
is this the largest such case?]


Boundary connections:

A039768:  gcd(phi(2009),2008) = tau(2008)

A125680:  31 Dec 2009 is the next Blue Moon