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

Author

R. H. Hardin, Sep 02 2011

Keywords

• nonn

Comments

Column 2 of A194778.

Examples

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

Links

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

Crossrefs

Cf. A194778.

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)