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Counts the ways to write 0 as 1 +- 2 +- 3 +- 4 +- ... +- k for some k, where signs alternate except that there is one instance of two consecutive positive terms.
0

%I #12 Aug 12 2020 01:30:29

%S 1,2,-3,1,-2,3,4,-5,6,-7,1,-2,3,-4,5,6,-7,8,-9,10,-11,1,-2,3,-4,5,-6,

%T 7,8,-9,10,-11,12,-13,14,-15,1,-2,3,-4,5,-6,7,-8,9,10,-11,12,-13,14,

%U -15,16,-17,18,-19,1,-2,3,-4,5,-6,7,-8,9,-10,11,12,-13,14,-15,16,-17,18,-19,20,-21,22,-23,1,-2,3,-4,5,-6,7,-8,9,-10,11

%N Counts the ways to write 0 as 1 +- 2 +- 3 +- 4 +- ... +- k for some k, where signs alternate except that there is one instance of two consecutive positive terms.

%C Derived from an attempt to demonstrate that the fundamental state of a ferromagnetic systems defined with the Hamiltonian defined in "A measure for the complexity of Boolean functions" has energy equal to -0.5.

%D L. Franco, Long-range ferromagnetic model in the hypercell. In preparation

%H L. Franco, <a href="https://arxiv.org/abs/cond-mat/0111169">A measure for the complexity of Boolean functions related to their implementation in neural networks</a>, arXiv:cond-mat/0111169 [cond-mat.dis-nn], 2001.

%e 0=1+2-3, 0=1-2+3+4-5+6-7, 0=1-2+3-4+5+6-7+8-9+10-11, ...

%K sign

%O 3,2

%A Leonardo Franco (Leonardo.Franco(AT)psy.ox.ac.uk), Oct 23 2002

%E Edited by _Joel B. Lewis_, Nov 15 2006