A194772 - OEIS

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.

%I #10 May 05 2018 08:24:00

%S 7,17,41,95,219,493,1101,2427,5311,11529,24881,53399,114083,242725,

%T 514581,1087411,2291335,4815681,10097401,21126863,44117867,91963997,

%U 191384541,397682155,825190479,1710033273,3539371201,7317351687

%N 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.

%C Column 2 of A194778.

%H R. H. Hardin, <a href="/A194772/b194772.txt">Table of n, a(n) for n = 1..34</a>

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

%F Conjectures from _Colin Barker_, May 05 2018: (Start)

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

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

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

%F (End)

%e All solutions for 3 X 3 including a 2.

%e ..0

%e ..1.1

%e ..1.1.2

%Y Cf. A194778.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 02 2011