A138017 Sequence generated by incidence matrix of the Fano plane, PG(2,2).

1, 3, 5, 15, 37, 111, 317, 951, 2821, 8463, 25325, 75975, 227797, 683391, 2049917, 6149751, 18448741, 55346223

Offset

1,2

Comments

a(n)/a(n-1) tends to 3, an eigenvalue of the matrix.

References

Mathworld (Projective plane).

Links

Table of n, a(n) for n=1..18.

Formula

Let X = the 7x7 incidence matrix of the Fano plane PG(2,2): [1,1,1,0,0,0,0; 1,0,0,1,1,0,0; 1,0,0,0,0,1,1; 0,1,0,1,0,1,0; 0,1,0,0,1,0,1; 0,0,1,1,0,0,1; 0,0,1,0,1,1,0]. a(n) = the upper left term in X^n.

Empirical a(n)=3*a(n-1)+2*a(n-2)-6*a(n-3). G.f.: x*(1-6*x^2)/(1-3*x-2*x^2+6*x^3). [Colin Barker, Jan 26 2012]

Example

a(5) = 37, the upper left term of X^5.

Crossrefs

Sequence in context: A146212 A265762 A018516 * A280764 A148503 A236571

Adjacent sequences: A138014 A138015 A138016 * A138018 A138019 A138020

Keyword

nonn

Author

Gary W. Adamson, Feb 28 2008

Status

approved