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Second differences of A074658, which counts the convex partitions of n.
2

%I #4 Jun 24 2014 01:08:26

%S 1,0,1,-1,2,0,-2,3,2,-4,3,2,-6,9,3,-13,6,12,-14,12,-1,-13,14,9,-14,8,

%T 4,-8,6,16,-37,35,10,-25,19,10,-45,34,30,-27,-8,35,-37,36,8,-37,21,37,

%U -51,53,1,-56,41,68,-79,13,29,-23,16,87,-98,40,38,-70,43,53,-81,81,35,-61,-28,140,-132,87,80,-118,5

%N Second differences of A074658, which counts the convex partitions of n.

%C Up to n=246, the signs of the terms show some periodicity (mod 3): a(3n) is almost always negative and a(3n+2) is almost always positive. Does this continue?

%F a(n) = A074659(n+1)-A074659(n) = A074658(n+2)-2*A074658(n+1)+A074658(n)

%t Table[a[n+2]-2a[n+1]+a[n], {n, 0, 76}] (* a[n] is defined in A074658. *)

%Y Cf. A074658, A074659.

%K sign

%O 0,5

%A _Dean Hickerson_, Aug 29 2002