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A138017
Expansion of g.f. x*(1-6*x^2)/(1-3*x-2*x^2+6*x^3).
0
1, 3, 5, 15, 37, 111, 317, 951, 2821, 8463, 25325, 75975, 227797, 683391, 2049917, 6149751, 18448741, 55346223, 166037645, 498112935, 1494336757, 4483010271, 13449026717, 40347080151, 121041232261, 363123696783, 1089371073965, 3268113221895, 9804339632917, 29413018898751
OFFSET
1,2
COMMENTS
Previous name was: Sequence generated by incidence matrix of the Fano plane, PG(2,2).
a(n)/a(n-1) tends to 3.
LINKS
Eric Weisstein's World of Mathematics, 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.
From Colin Barker, Jan 26 2012: (Start)
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). (End)
a(n) ~ 3^n / 7. - Vaclav Kotesovec, Aug 21 2025
PROG
(PARI) a(n) = ([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]^n)[1, 1]; \\ Michel Marcus, Aug 21 2025
CROSSREFS
Sequence in context: A146212 A265762 A018516 * A280764 A148503 A236571
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Feb 28 2008
EXTENSIONS
More terms from Michel Marcus, Aug 21 2025
New name using existing formula from Joerg Arndt, Aug 21 2025
STATUS
approved