cp's OEIS Frontend

A242545 Number of length n+3 0..4 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..4 introduced in 0..4 order.

%I A242545 #8 Jan 01 2024 19:53:41
%S A242545 13,43,165,690,3050,13988,65588,311431,1489435,7152787,34431086,
%T A242545 165959996,800539194,3863197403,18647303797,90021133115,434616726192,
%U A242545 2098395654912,10131623972784,48918915963483,236198983546635
%N A242545 Number of length n+3 0..4 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..4 introduced in 0..4 order.
%C A242545 Column 4 of A242549.
%H A242545 R. H. Hardin, <a href="/A242545/b242545.txt">Table of n, a(n) for n = 1..210</a>
%F A242545 Empirical: a(n) = 7*a(n-1) -14*a(n-2) +29*a(n-3) -53*a(n-4) -18*a(n-5) -28*a(n-6) -56*a(n-7) +140*a(n-8) +176*a(n-9) +192*a(n-10) +192*a(n-11) +64*a(n-12).
%F A242545 Empirical: G.f.:  -x*(13 -48*x +46*x^2 -240*x^3 -28*x^4 +26*x^5 +245*x^6 +1169*x^7 +1276*x^8 +1240*x^9 +992*x^10 +296*x^11) / ( (2*x^2+2*x-1) *(x^2+x-1) *(2*x^2+1) *(x^2+1) *(4*x^2+1) *(4*x^2+4*x-1) ). - _R. J. Mathar_, May 18 2014
%e A242545 Some solutions for n=4
%e A242545 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A242545 ..1....1....1....0....1....1....1....1....1....0....0....1....1....1....1....1
%e A242545 ..2....2....0....1....2....1....1....2....0....1....0....2....2....2....2....2
%e A242545 ..1....3....2....2....3....2....2....3....2....2....1....3....3....1....1....3
%e A242545 ..3....2....1....0....3....3....3....2....0....3....2....3....0....2....1....3
%e A242545 ..1....3....2....3....1....2....0....1....2....2....3....0....1....0....2....3
%e A242545 ..0....3....1....3....2....4....0....3....0....2....3....1....4....0....3....1
%Y A242545 Cf. A242549.
%K A242545 nonn
%O A242545 1,1
%A A242545 _R. H. Hardin_, May 17 2014