A203437 Number of nX2 0..7 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors

1, 8, 64, 372, 2528, 21988, 186348, 1484834, 11983672, 99287560, 822775984, 6775991390, 55862871172, 461924799782, 3821399789826, 31599121605851, 261335463668876, 2162179173512322, 17891459865015592, 148048457731612474

Offset

1,2

Comments

Column 2 of A203443

Links

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

Formula

Empirical: a(n) = 36*a(n-1) -602*a(n-2) +6524*a(n-3) -53347*a(n-4) +352422*a(n-5) -1940764*a(n-6) +9153172*a(n-7) -37752485*a(n-8) +137893274*a(n-9) -452055467*a(n-10) +1342970830*a(n-11) -3638057933*a(n-12) +9071693523*a(n-13) -20876148243*a(n-14) +44616933604*a(n-15) -89039926643*a(n-16) +165518375256*a(n-17) -290731468771*a(n-18) +476018515556*a(n-19) -741344186335*a(n-20) +1086274377944*a(n-21) -1492483448334*a(n-22) +2010607579832*a(n-23) -2375704774615*a(n-24) +3083242158195*a(n-25) -2965069704481*a(n-26) +3977509164220*a(n-27) -2865245806362*a(n-28) +4282022816454*a(n-29) -2209936530089*a(n-30) +3563239284535*a(n-31) -1810789629749*a(n-32) +1541595407413*a(n-33) -2532133018233*a(n-34) -1528699238219*a(n-35) -4363095870912*a(n-36) -4657280718765*a(n-37) -6241687618075*a(n-38) -6583983672912*a(n-39) -6941720583956*a(n-40) -6657522110347*a(n-41) -6088912229602*a(n-42) -5251969355432*a(n-43) -4291270339013*a(n-44) -3336195568667*a(n-45) -2461322964502*a(n-46) -1730540685280*a(n-47) -1157304679412*a(n-48) -737378430538*a(n-49) -447345400723*a(n-50) -258349758641*a(n-51) -142008774910*a(n-52) -74211080092*a(n-53) -36849518988*a(n-54) -17360164987*a(n-55) -7748606740*a(n-56) -3270826347*a(n-57) -1302550490*a(n-58) -488139432*a(n-59) -171539870*a(n-60) -56301911*a(n-61) -17173472*a(n-62) -4836189*a(n-63) -1247724*a(n-64) -291715*a(n-65) -60925*a(n-66) -11148*a(n-67) -1730*a(n-68) -217*a(n-69) -20*a(n-70) -a(n-71)

Example

Some solutions for n=5
..1..1....0..0....4..4....5..5....2..2....5..5....0..0....5..5....1..1....3..3
..4..4....5..5....4..4....7..7....5..5....5..5....1..1....5..5....1..1....3..3
..4..4....6..6....6..6....7..7....5..5....3..1....4..4....3..3....4..4....1..0
..5..5....6..6....6..6....1..1....0..0....3..3....6..6....1..1....4..4....4..4
..5..5....0..0....4..4....0..0....0..0....3..3....6..6....0..0....2..2....4..4

Crossrefs

Sequence in context: A225014 A228460 A202909 * A224132 A297376 A293888

Adjacent sequences: A203434 A203435 A203436 * A203438 A203439 A203440

Keyword

nonn

Author

R. H. Hardin Jan 01 2012

Status

approved