This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209042 Number of n X 3 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it. 1

%I

%S 36,1300,47700,1752148,64369764,2364812680,86878417604,3191736905988,

%T 117257942776700,4307819083344444,158260539240359944,

%U 5814171346741659592,213600867349885236600,7847262801829583566600,288292525423375500733688

%N Number of n X 3 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

%C Column 3 of A209047.

%H R. H. Hardin, <a href="/A209042/b209042.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A209042/a209042_1.pdf">Maple-assisted proof of empirical formula</a>

%F Empirical: a(n) = 23*a(n-1) +491*a(n-2) +570*a(n-3) -2219*a(n-4) -7882*a(n-5) -12517*a(n-6) -6376*a(n-7) -1205*a(n-8) -6747*a(n-9) +4080*a(n-10) +7811*a(n-11) -4675*a(n-12) +1790*a(n-13) +2576*a(n-14) -2905*a(n-15) +513*a(n-16) +621*a(n-17) -27*a(n-18) -81*a(n-19).

%F Formula confirmed by _Robert Israel_, Apr 03 2018 (see link).

%e Some solutions for n=4

%e ..0..1..0....0..1..2....2..1..2....2..0..1....1..0..2....1..3..0....1..0..1

%e ..3..3..2....3..3..0....3..0..2....0..2..0....3..2..1....2..1..3....0..1..3

%e ..1..3..1....0..1..1....2..0..0....1..2..2....1..0..3....0..1..0....1..2..1

%e ..2..3..3....3..3..1....1..3..0....3..0..0....3..0..1....1..2..0....0..2..3

%Y Cf. A209047.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 21:00 EST 2019. Contains 329937 sequences. (Running on oeis4.)