A138017 Expansion of g.f. x*(1-6*x^2)/(1-3*x-2*x^2+6*x^3).

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

Table of n, a(n) for n=1..30.

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

Adjacent sequences: A138014 A138015 A138016 * A138018 A138019 A138020

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