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