[seqfan] Re: Column Recurrences of Fibonacci Order = Tilings

[Ron Hardin]

If you omit the requirement that the upper left corner = 1,  then you get binary matrices with no h,v,or nw-se adjacent 1's

Table starts
...2....3......5.......8.......13........21........34........55........89
...3....6.....13......28.......60.......129.......277.......595......1278
...5...13.....42.....126......387......1180......3606.....11012.....33636
...8...28....126.....524.....2229......9425.....39905....168925....715072
..13...60....387....2229....13322.....78661....466288...2760690..16350693
..21..129...1180....9425....78661....647252...5350080..44159095.364647622
..34..277...3606...39905...466288...5350080..61758332.711479843..........
..55..595..11012..168925..2760690..44159095.711479843....................
..89.1278..33636..715072.16350693.364647622..............................
.144.2745.102733.3027049.96830726........................................

which is http://oeis.org/A226444  , conceived as a tiling with rows/columns all over OEIS, omitting two rows and columns of 1's.

The same recurrences seem to work for these rows and columns too and perhaps are simpler theoretically.
Anyway they could be entered as proven on the various sequences thereby linked, assuming the proof generalizes without the upper left 1.



 
rhhardin at mindspring.com
rhhardin at att.net (either)