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A138017
Sequence generated by incidence matrix of the Fano plane, PG(2,2).
0
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).
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
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Feb 28 2008
STATUS
approved