A196807 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4

1, 41, 420, 8719, 166682, 2535368, 46685074, 822353649, 14219232895, 247793610490, 4321118145913, 75358654335980, 1315206264464536, 22934359993226090, 399880131880385285, 6973750320639071161

Offset

1,2

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's

Column 6 of A196809

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +81*a(n-2) +1187*a(n-3) +14009*a(n-4) +152601*a(n-5) +972831*a(n-6) +1112105*a(n-7) -15436914*a(n-8) -72110331*a(n-9) -142326597*a(n-10) -991340283*a(n-11) -547633934*a(n-12) +16220401435*a(n-13) +20288910387*a(n-14) +2885028194*a(n-15) +368091443331*a(n-16) -1230469139652*a(n-17) -1955748191845*a(n-18) -916989452296*a(n-19) -20894508968521*a(n-20) +102899177075844*a(n-21) +64658065178654*a(n-22) -86252448610683*a(n-23) +3995043990057793*a(n-24) -13212680295761472*a(n-25) +11723249089236806*a(n-26) -17552499231979387*a(n-27) -160267711456330981*a(n-28) +525218212810881548*a(n-29) -573999045950482216*a(n-30) -334216597215077028*a(n-31) +9603972602378184406*a(n-32) -40244536999676938658*a(n-33) +117636762994743535342*a(n-34) -300575655937989219752*a(n-35) +587416616200388511329*a(n-36) -942757838826774568207*a(n-37) +1328885545845745047126*a(n-38) -1334572810933812145830*a(n-39) +1028054676357174733785*a(n-40) -854575907062291150449*a(n-41) -1011829624515934604803*a(n-42) +4701332553608363074901*a(n-43) -6832212290502712893095*a(n-44) +7502475094241840182160*a(n-45) -6734631935365713227978*a(n-46) +11868475287395189767435*a(n-47) -27215358415341998659721*a(n-48) +22412873289397146927366*a(n-49) -16108608991801633690875*a(n-50) +56970216675059509502782*a(n-51) -43457227880491589807962*a(n-52) -36607628796861286486714*a(n-53) -2585733147078693658147*a(n-54) +41407704226336920009933*a(n-55) +52715095931971737825423*a(n-56) -6138505750133038229708*a(n-57) -103708455511843309729639*a(n-58) +30684433520799082291050*a(n-59) -30258518023038983364839*a(n-60) +73140231874272363580745*a(n-61) +42872704759446098960495*a(n-62) -52008221241581236423762*a(n-63) +7556215203773523028438*a(n-64) -87196011625060565892570*a(n-65) +38724935200198777167388*a(n-66) +39385209467687328287040*a(n-67) +20008287306966500986968*a(n-68) +3843148667954450581176*a(n-69) -40773041066419728284240*a(n-70) -7924252907590517421600*a(n-71) +5915487932709333518304*a(n-72) +9402823819578807287648*a(n-73) +4419858399723745600256*a(n-74) -3134270370848713084736*a(n-75) -2181849523161360597760*a(n-76) -66187958852564400960*a(n-77) +229799792265042353408*a(n-78) +436838529210528607232*a(n-79) +115823154907594984448*a(n-80) +69728018986375031296*a(n-81) -27799436701604930048*a(n-82) -12413139972899878912*a(n-83) +3078113712557976576*a(n-84) +2698559738789154816*a(n-85) +2357714578735861760*a(n-86) -1408084157308383232*a(n-87) -1175976409943556096*a(n-88) -612407658040852480*a(n-89) -309485038454308864*a(n-90) -67014717934862336*a(n-91) +2662830364164096*a(n-92) +610107496333312*a(n-93) +3871662258782208*a(n-94) +192094138269696*a(n-95) +266485389852672*a(n-96) -7176563195904*a(n-97) -16755002966016*a(n-98)

Example

Some solutions for n=4
..0..3..0..0..0..0....0..0..0..0..3..0....0..3..0..0..0..0....0..3..0..0..3..0
..0..0..0..0..3..0....0..3..2..3..0..3....3..0..0..3..0..0....0..0..3..2..0..0
..0..0..0..3..2..1....0..0..1..0..0..0....0..0..0..3..0..0....3..0..0..3..0..3
..0..3..0..0..0..0....0..0..0..0..3..0....0..0..0..0..3..0....0..3..0..0..3..0

Crossrefs

Sequence in context: A178387 A068849 A145293 * A267325 A083761 A209823

Adjacent sequences: A196804 A196805 A196806 * A196808 A196809 A196810

Keyword

nonn

Author

R. H. Hardin Oct 06 2011

Status

approved