A205359 - OEIS

A205359

Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.

%I #7 Oct 29 2022 15:09:58

%S 12290,296774,7690946,216561893,6379775618,194089073306,6018114334610,

%T 188843661927722,5967907867992530,189409387169327072,

%U 6026765613077397218,192055334303544833636,6125756449825618892738,195490687107317681212208

%N Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.

%C Column 6 of A205361.

%H R. H. Hardin, <a href="/A205359/b205359.txt">Table of n, a(n) for n = 1..170</a>

%F Empirical: a(n) = 129*a(n-1) -6829*a(n-2) +180102*a(n-3) -1812314*a(n-4) -26965888*a(n-5) +1058318461*a(n-6) -10846886378*a(n-7) -49737480772*a(n-8) +2295355105568*a(n-9) -18015178836383*a(n-10) -81864164506822*a(n-11) +2394566895549460*a(n-12) -11860018021894482*a(n-13) -84593338120198865*a(n-14) +1268674307807101798*a(n-15) -2993333202250939507*a(n-16) -43051010280497156149*a(n-17) +341429153639679616892*a(n-18) -45182088406779755008*a(n-19) -10747883589487327567286*a(n-20) +45407942329939110249282*a(n-21) +94798848953136840186932*a(n-22) -1349716443574942564109868*a(n-23) +2722174384120704282858588*a(n-24) +14735009522112986954734572*a(n-25) -86296064594459279392611216*a(n-26) +46485242928023619513093696*a(n-27) +906523618561887787562803320*a(n-28) -2813279876510177273448972456*a(n-29) -1530571404542996352937541472*a(n-30) +26326465115738100154601783472*a(n-31) -47360603883548156181434367552*a(n-32) -61647618225907205976346123104*a(n-33) +375747310424617199628435745920*a(n-34) -446498229621925445844720272832*a(n-35) -628397187497024225745447156096*a(n-36) +2585362650894549622026434504448*a(n-37) -2738003990855811474605393249280*a(n-38) -1235887284475709428755606497280*a(n-39) +6897904050968209366755169536000*a(n-40) -8943912639051762003563564236800*a(n-41) +6134476476453351777682587648000*a(n-42) -2276953194824626073115820032000*a(n-43) +362304695886258077077340160000*a(n-44).

%e Some solutions for n=4

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

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

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

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

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

%Y Cf. A205361.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 26 2012