A163012 Number of n X 3 binary arrays with all 1s connected and a path of 1s from top row to lower right corner.

3, 16, 82, 416, 2103, 10633, 53767, 271882, 1374808, 6951884, 35153031, 177755487, 898841773, 4545100350, 22982840520, 116215466582, 587657328849, 2971559176087, 15026042394605, 75980970481664, 384206813990810, 1942787450345722, 9823935806901973, 49675899811351245

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000 (terms 1..100 from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (7,-11,6,1,-7,1).

Formula

Empirical: a(n)= 7*a(n-1) -11*a(n-2) +6*a(n-3) +a(n-4) -7*a(n-5) +a(n-6). - R. J. Mathar, Aug 11 2009

Formula confirmed using the transfer matrix method. - Andrew Howroyd, Dec 24 2025

G.f.: x*(3 - 5*x + 3*x^2 - 6*x^4 + x^5)/(1 - 7*x + 11*x^2 - 6*x^3 - x^4 + 7*x^5 - x^6). - Andrew Howroyd, Dec 24 2025

Crossrefs

Column 3 of A391489.

Sequence in context: A072615 A020871 A037780 * A164100 A041707 A037584

Adjacent sequences: A163009 A163010 A163011 * A163013 A163014 A163015

Keyword

nonn,easy

Author

R. H. Hardin, Jul 20 2009

Status

approved