A076645 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.

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

Offset

3,2

Comments

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.

References

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

Links

Table of n, a(n) for n=3..91.

L. Franco, A measure for the complexity of Boolean functions related to their implementation in neural networks, arXiv:cond-mat/0111169 [cond-mat.dis-nn], 2001.

Example

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

Crossrefs

Sequence in context: A124171 A276146 A210530 * A350604 A011448 A174981

Adjacent sequences: A076642 A076643 A076644 * A076646 A076647 A076648

Keyword

sign

Author

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

Extensions

Edited by Joel B. Lewis, Nov 15 2006

Status

approved