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A204475 Number of (n+2)X3 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..3 introduced in row major order 1

%I #6 Mar 31 2012 12:37:01

%S 80,307,1157,1899,7191,24718,70726,277992,996500,3558732,13565616,

%T 51046854,192347648,730397369,2770971357,10530282255,40019308588,

%U 152140400520,578605689115,2200549646588,8369694858448,31835066870337

%N Number of (n+2)X3 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..3 introduced in row major order

%C Column 1 of A204483

%H R. H. Hardin, <a href="/A204475/b204475.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) -21*a(n-2) +22*a(n-3) -22*a(n-4) +60*a(n-5) -12*a(n-6) -448*a(n-7) +1866*a(n-8) -6498*a(n-9) +15684*a(n-10) -22888*a(n-11) +31417*a(n-12) -57462*a(n-13) +52230*a(n-14) +113688*a(n-15) -424149*a(n-16) +557158*a(n-17) -411880*a(n-18) +403956*a(n-19) -471132*a(n-20) -17430*a(n-21) +839565*a(n-22) -1046718*a(n-23) +545742*a(n-24) -113292*a(n-25) +131571*a(n-26) -347004*a(n-27) +373977*a(n-28) -80190*a(n-29) -271188*a(n-30) +354294*a(n-31) -190269*a(n-32) +39366*a(n-33)

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 15 2012

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)