A183627 - OEIS

%I #17 Apr 02 2018 06:16:53

%S 309,447,741,1383,2829,6207,14421,35223,89949,238767,654501,1840263,

%T 5274669,15332127,45012981,133072503,395284989,1177990287,3518241861,

%U 10523267943,31506888909,94394837247,282932853141,848295242583

%N Number of (n+1) X 5 0..2 arrays with every 2 x 2 subblock summing to 4.

%C Column 4 of A183632.

%H R. H. Hardin, <a href="/A183627/b183627.txt">Table of n, a(n) for n = 1..200</a>

%H Robert Israel, <a href="/A183627/a183627.pdf">Maple-assisted proof of empirical formula</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).

%F Conjectures from _Colin Barker_, Mar 30 2018: (Start)

%F G.f.: 3*x*(103 - 469*x + 486*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

%F a(n) = 3*(60 + 5*2^(2+n) + 3^n).

%F (End)

%F Formula and conjectures confirmed by _Robert Israel_, Mar 30 2018 (see link).

%e Some solutions for 3 X 5:

%e   2 1 2 0 2    0 2 1 2 1    1 1 0 2 0    2 0 1 2 0

%e   1 0 1 1 1    2 0 1 0 1    1 1 2 0 2    0 2 1 0 2

%e   1 2 1 1 1    0 2 1 2 1    1 1 0 2 0    2 0 1 2 0

%p seq(3*(60 + 5*2^(2+n) + 3^n),n=1..30); # _Robert Israel_, Mar 30 2018

%Y Cf. A183632.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011