A214113 Number of 0..3 colorings of a 2X(n+1) array circular in the n+1 direction with new values 0..3 introduced in row major order.

4, 11, 111, 670, 4994, 34041, 241021, 1678940, 11777184, 82366471, 576786731, 4036842810, 28259892574, 197813269301, 1384710821241, 9692921940280, 67850615007164, 474953820774531, 3324678198248551, 23272743029259350

Offset: 1

Author

R. H. Hardin Jul 04 2012

Keywords

• nonn

Comments

Row 2 of A214112

Examples

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

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +22*a(n-2) -4*a(n-3) -21*a(n-4).

Empirical: G.f. -x*(7*x+4)*(3*x-1) / ( (x-1)*(3*x+1)*(7*x-1)*(1+x) ), a(n) = 11/24 +3*(-1)^(n+1)/8 +7^(n+1)/24 +(-3)^(n+1)/8. - R. J. Mathar, Jul 04 2012