A194772 Number of lower triangles of an (n+2) X (n+2) 0..2 array with new values introduced in row major order 0..2 and no element unequal to more than one horizontal or vertical neighbor.

7, 17, 41, 95, 219, 493, 1101, 2427, 5311, 11529, 24881, 53399, 114083, 242725, 514581, 1087411, 2291335, 4815681, 10097401, 21126863, 44117867, 91963997, 191384541, 397682155, 825190479, 1710033273, 3539371201, 7317351687

Offset

1,1

Comments

Column 2 of A194778.

Links

R. H. Hardin, Table of n, a(n) for n = 1..34

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5).

Conjectures from Colin Barker, May 05 2018: (Start)

G.f.: x*(7 - 4*x - 17*x^2 + 4*x^3 + 12*x^4) / ((1 - x)*(1 + x)^2*(1 - 2*x)^2).

a(n) = (-3*n + 2^(n+3)*(3*n+8) + 17) / 27 for n even.

a(n) = (3*n + 2^(n+3)*(3*n+8) + 10) / 27 for n odd.

(End)

Example

All solutions for 3 X 3 including a 2.
..0
..1.1
..1.1.2

Crossrefs

Cf. A194778.

Sequence in context: A360428 A193214 A184862 * A193546 A268255 A124965

Adjacent sequences: A194769 A194770 A194771 * A194773 A194774 A194775

Keyword

nonn

Author

R. H. Hardin, Sep 02 2011

Status

approved