cp's OEIS Frontend

A203650 1/25 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

%I A203650 #8 Jun 04 2018 12:08:44
%S A203650 81,1517,28057,519445,9616161,178019197,3295578857,61009378085,
%T A203650 1129435635441,20908668388877,387071560403257,7165659241743925,
%U A203650 132654210800937921,2455760042384774557,45462238622967429257
%N A203650 1/25 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
%C A203650 Column 2 of A203656.
%H A203650 R. H. Hardin, <a href="/A203650/b203650.txt">Table of n, a(n) for n = 1..210</a>
%F A203650 Empirical: a(n) = 17*a(n-1) +28*a(n-2).
%F A203650 Conjectures from _Colin Barker_, Jun 04 2018: (Start)
%F A203650 G.f.: x*(81 + 140*x) / (1 - 17*x - 28*x^2).
%F A203650 a(n) = (2^(-1-n)*((17-sqrt(401))^n*(-77+5*sqrt(401)) + (17+sqrt(401))^n*(77+5*sqrt(401))))/sqrt(401).
%F A203650 (End)
%e A203650 Some solutions for n=4:
%e A203650 ..3..1..2....3..4..3....2..2..1....0..3..2....2..0..1....4..4..4....1..2..4
%e A203650 ..4..3..1....1..3..2....3..2..2....3..4..3....4..2..0....2..4..4....3..1..2
%e A203650 ..2..4..3....2..1..3....1..3..2....3..3..3....1..4..2....1..2..4....0..3..1
%e A203650 ..2..2..4....3..2..1....0..1..3....4..3..4....0..1..4....1..1..2....2..0..3
%e A203650 ..1..2..2....2..4..2....4..0..1....4..4..1....1..3..1....0..1..1....0..4..0
%Y A203650 Cf. A203656.
%K A203650 nonn
%O A203650 1,1
%A A203650 _R. H. Hardin_, Jan 04 2012