A220227 Majority value maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 2 X n array.

1, 6, 18, 51, 157, 477, 1445, 4384, 13297, 40332, 122339, 371085, 1125588, 3414184, 10356065, 31412486, 95281776, 289013030, 876647491, 2659087097, 8065664119, 24465139829, 74208776604, 225093441705, 682763681270, 2070989900565

Offset

1,2

Comments

Row 2 of A220226.

Links

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

Formula

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

Empirical g.f.: x*(1 - x)*(1 + 2*x)^2*(1 + x^2)*(1 + x + x^2) / (1 - 2*x - x^2 - 6*x^3 - x^4 - 3*x^5 + 4*x^6 + 2*x^7 + 4*x^8). - Colin Barker, Jul 31 2018

Example

Some solutions for n=3:
..1..1..0....1..1..1....1..0..0....1..0..1....0..1..0....0..1..1....1..1..1
..1..1..0....1..0..1....0..0..0....1..1..1....1..1..1....0..1..1....0..1..0

Crossrefs

Cf. A220226.

Sequence in context: A328534 A003290 A318160 * A075650 A015645 A001216

Adjacent sequences: A220224 A220225 A220226 * A220228 A220229 A220230

Keyword

nonn

Author

R. H. Hardin Dec 08 2012

Status

approved