A219737 Unmatched value maps: number of n X 4 binary arrays indicating the locations of corresponding elements not equal to any horizontal, vertical or antidiagonal neighbor in a random 0..1 n X 4 array.

7, 28, 126, 524, 2229, 9425, 39905, 168925, 715072, 3027049, 12813931, 54243509, 229621433, 972024617, 4114736810, 17418344167, 73734658344, 312130693269, 1321299533915, 5593273893746, 23677229915913, 100229530526756

Offset

1,1

Comments

Column 4 of A219741.

Links

R. H. Hardin, Table of n, a(n) for n = 1..130

Formula

Empirical: a(n) = a(n-1) + 10*a(n-2) + 15*a(n-3) + 4*a(n-4) - 6*a(n-5) - a(n-6) + 3*a(n-7) - a(n-8) for n>9.

Zeilberger's Maple code (see links in A228285) would give a proof that this recurrence is correct. - N. J. A. Sloane, Aug 22 2013

G.f.: x*(1 + x)*(7 + 14*x + 14*x^2 - x^3 - 2*x^4 - 2*x^5 + 3*x^6 - x^7) / (1 - x - 10*x^2 - 15*x^3 - 4*x^4 + 6*x^5 + x^6 - 3*x^7 + x^8). - Colin Barker, Mar 12 2018

Example

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

Crossrefs

Cf. A219741.

Sequence in context: A303406 A054626 A220361 * A316106 A359203 A354456

Adjacent sequences: A219734 A219735 A219736 * A219738 A219739 A219740

Keyword

nonn

Author

R. H. Hardin, Nov 26 2012

Status

approved