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.

13, 43, 165, 690, 3050, 13988, 65588, 311431, 1489435, 7152787, 34431086, 165959996, 800539194, 3863197403, 18647303797, 90021133115, 434616726192, 2098395654912, 10131623972784, 48918915963483, 236198983546635

Offset: 1

Author

R. H. Hardin, May 17 2014

Keywords

• nonn

Comments

Column 4 of A242549.

Examples

			Some solutions for n=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....1....1....0....0....1....1....1....1....1
..2....2....0....1....2....1....1....2....0....1....0....2....2....2....2....2
..1....3....2....2....3....2....2....3....2....2....1....3....3....1....1....3
..3....2....1....0....3....3....3....2....0....3....2....3....0....2....1....3
..1....3....2....3....1....2....0....1....2....2....3....0....1....0....2....3
..0....3....1....3....2....4....0....3....0....2....3....1....4....0....3....1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A242549.

Formula

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).

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