A204522 - OEIS

%I #6 Mar 31 2012 12:37:02

%S 3700,99975,2838990,72357582,1908820114,51725097532,1365072053705,

%T 36097389558491,963601913333651,25587580363278980,678631104416699064,

%U 18046297209664043910,479517671229129135064,12732949974318602571176

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

%C Column 1 of A204525

%H R. H. Hardin, <a href="/A204522/b204522.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 19*a(n-1) +20*a(n-2) +6715*a(n-3) -39400*a(n-4) -278721*a(n-5) -566831*a(n-6) -4070692*a(n-7) +120891967*a(n-8) +449176991*a(n-9) -2026661677*a(n-10) -12813924036*a(n-11) -26746085584*a(n-12) +9786213012*a(n-13) +884506182436*a(n-14) +5741310584350*a(n-15) -3455066401652*a(n-16) -69861234867780*a(n-17) -169629596856776*a(n-18) -60851219675756*a(n-19) +1748089724633264*a(n-20) +3473211354730872*a(n-21) +9499905146549464*a(n-22) +3113390646548208*a(n-23) -124798919635015376*a(n-24) -237138944821841424*a(n-25) +133795161307775232*a(n-26) -71068703870450688*a(n-27) +4068396008822617920*a(n-28) +376322753879088768*a(n-29) -4563721857649730688*a(n-30) -361633579086451968*a(n-31) -41875485211919288448*a(n-32) +47298545358942585600*a(n-33) -6639913657255177728*a(n-34) +18106112374211584512*a(n-35) +150992321107533290496*a(n-36) -302390206675970669568*a(n-37) +278083184567959664640*a(n-38) -232178806239185018880*a(n-39) -169014772365536894976*a(n-40) +474715662297209634816*a(n-41) -421697490050246639616*a(n-42) +297839000295167754240*a(n-43) -49361960604404809728*a(n-44) -68780555329635090432*a(n-45) +24179394483616481280*a(n-46) for n>49

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 15 2012