A245161 Number of length n 0..6 arrays with new values introduced in order from both ends.

1, 1, 2, 4, 9, 23, 65, 199, 654, 2296, 8569, 33825, 140581, 612933, 2795181, 13298407, 65851100, 338654554, 1805083341, 9952373825, 56645932971, 332111798479, 2000990363889, 12357518954759, 78010845456554, 501994699807228

Offset

1,3

Links

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

Formula

Empirical: a(n) = 37*a(n-1) - 605*a(n-2) + 5765*a(n-3) - 35523*a(n-4) + 148371*a(n-5) - 427775*a(n-6) + 849335*a(n-7) - 1134976*a(n-8) + 969292*a(n-9) - 474720*a(n-10) + 100800*a(n-11) for n>12.

Empirical g.f.: x*(1 - 36*x + 570*x^2 - 5230*x^3 + 30829*x^4 - 122268*x^5 + 332049*x^6 - 616386*x^7 + 767435*x^8 - 616428*x^9 + 296529*x^10 - 69446*x^11) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)^2*(1 - 5*x)^2*(1 - 7*x)). - Colin Barker, Nov 03 2018

Example

Some solutions for n=7:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....1....1....1....1....1....0....1....1....1....1....0....1....1
..0....1....1....1....1....0....1....0....0....2....2....2....1....0....0....1
..1....1....0....0....2....1....2....1....1....2....2....2....0....1....2....0
..0....0....1....1....1....0....1....2....1....0....1....2....0....1....1....0
..0....1....1....0....0....1....1....1....1....1....1....1....0....0....0....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Column 6 of A245163.

Sequence in context: A245158 A245159 A245160 * A245162 A007476 A202552

Adjacent sequences: A245158 A245159 A245160 * A245162 A245163 A245164

Keyword

nonn

Author

R. H. Hardin, Jul 12 2014

Status

approved