A251215 Number of (n+1)X(4+1) 0..1 arrays with no 2X2 subblock having zero or two 1s

115, 589, 3089, 16911, 91777, 502971, 2746607, 15040763, 82261821, 450304289, 2463907651, 13485492509, 73797670811, 403887709287, 2210318878259, 12096617815013, 66200984952569, 362301557191539, 1982772302106141

Offset

1,1

Comments

Column 4 of A251219

Links

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

Formula

Empirical: a(n) = 6*a(n-1) +22*a(n-2) -157*a(n-3) -115*a(n-4) +1491*a(n-5) -328*a(n-6) -6480*a(n-7) +4148*a(n-8) +13794*a(n-9) -11784*a(n-10) -13976*a(n-11) +13612*a(n-12) +6008*a(n-13) -6440*a(n-14) -768*a(n-15) +960*a(n-16).

Empirical: G.f.: -x*(115 -101*x -2975*x^2 +3474*x^3 +28051*x^4 -38490*x^5 -120530*x^6 +182206*x^7 +251282*x^8 -409920*x^9 -244852*x^10 +435820*x^11 +97696*x^12 -200768*x^13 -9984*x^14 +30208*x^15) / ( -1 +6*x +22*x^2 -157*x^3 -115*x^4 +1491*x^5 -328*x^6 -6480*x^7 +4148*x^8 +13794*x^9 -11784*x^10 -13976*x^11 +13612*x^12 +6008*x^13 -6440*x^14 -768*x^15 +960*x^16 ). - R. J. Mathar, May 12 2016

Example

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

Crossrefs

Sequence in context: A334345 A255143 A154070 * A218324 A258673 A287430

Adjacent sequences: A251212 A251213 A251214 * A251216 A251217 A251218

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved