A220538 Equals one maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 2 X n array.

1, 4, 5, 25, 55, 166, 446, 1240, 3377, 9220, 25086, 68225, 185272, 502739, 1363404, 3696113, 10016803, 27140032, 73522056, 199146450, 539371804, 1460744681, 3955838351, 10712401393, 29008375808, 78550919660, 212702540041

Offset

1,2

Comments

Row 2 of A220537.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +3*a(n-3) -a(n-4) -7*a(n-5) -7*a(n-6) +7*a(n-8) -6*a(n-9) for n>12.

Empirical g.f.: x*(1 - 7*x^2 + 18*x^3 - 36*x^4 + 42*x^5 - 33*x^6 + 43*x^7 - 39*x^8 + 38*x^9 - 24*x^10 + 9*x^11) / ((1 + x)*(1 - 2*x)*(1 - 3*x + 3*x^2 - 6*x^3 + x^4 - 4*x^5 + 5*x^6 - 3*x^7)). - Colin Barker, Jul 31 2018

Example

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

Crossrefs

Cf. A220537.

Sequence in context: A164054 A333321 A047168 * A187996 A144053 A084465

Adjacent sequences: A220535 A220536 A220537 * A220539 A220540 A220541

Keyword

nonn

Author

R. H. Hardin, Dec 15 2012

Status

approved