A202442 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

224, 376, 676, 1102, 1722, 2544, 3652, 5054, 6850, 9048, 11764, 15006, 18906, 23472, 28852, 35054, 42242, 50424, 59780, 70318, 82234, 95536, 110436, 126942, 145282, 165464, 187732, 212094, 238810, 267888, 299604, 333966, 371266, 411512, 455012

Offset

1,1

Comments

Column 3 of A202447.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7) for n>8.

Conjectures from Colin Barker, May 29 2018: (Start)

G.f.: 2*x*(112 - 148*x - 114*x^2 + 285*x^3 - 74*x^4 - 122*x^5 + 84*x^6 - 15*x^7) / ((1 - x)^5*(1 + x)^2).

a(n) = (n^4 + 24*n^3 + 149*n^2 + 492*n + 468) / 6 for n even.

a(n) = (n^4 + 24*n^3 + 149*n^2 + 498*n + 492) / 6 for n>1 and odd.

(End)

Example

Some solutions for n=4:
..1..1..1..1..1....0..1..0..1..1....1..1..1..1..1....1..1..1..1..1
..0..1..0..0..0....1..1..1..1..1....1..0..0..0..0....1..0..1..0..0
..0..1..1..1..1....0..1..1..1..1....1..1..1..1..1....1..0..1..1..1
..0..1..0..1..1....1..1..1..1..1....1..0..1..0..1....1..0..1..1..1
..0..1..0..1..1....1..1..1..1..1....1..1..1..1..1....1..0..1..1..1
..0..1..0..1..1....1..1..1..1..1....1..1..1..1..1....1..0..1..1..1

Crossrefs

Cf. A202447.

Sequence in context: A046296 A240529 A177770 * A331371 A094209 A158227

Adjacent sequences: A202439 A202440 A202441 * A202443 A202444 A202445

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved