# [seqfan] A210662 et al

Ron Hardin rhhardin at att.net
Sun Dec 9 11:48:33 CET 2012

```This configuration of neighbors (h&v) seems to give http://oeis.org/A210662 ...
in which case some of the references could be linked in there, except
it's not clear what to call a column in by-rows format.

If the linked problems are in fact all the same, one could add b-files and
empirical recurrences to those.

==

T(n,k)=Number of ways to reciprocally link elements of an nXk array either to
themselves or to exactly one horizontal or vertical neighbor

Table starts
...1......2..........3.............5.................8...................13
...2......7.........22............71...............228..................733
...3.....22........131...........823..............5096................31687
...5.....71........823.........10012............120465..............1453535
...8....228.......5096........120465...........2810694.............65805403
..13....733......31687.......1453535..........65805403...........2989126727
..21...2356.....196785......17525619........1539222016.........135658637925
..34...7573....1222550.....211351945.......36012826776........6158217253688
..55..24342....7594361....2548684656......842518533590......279533139565077
..89..78243...47177097...30734932553....19711134149599....12688781322524383
.144.251498..293066688..370635224561...461148537211748...575975678462394151
.233.808395.1820552297.4469527322891.10788744980331535.26145024935911561519

Diagonal is A028420
Column 1 is A000045(n+1)
Column 2 is A030186
Column 3 is A033506(n-1)
Column 4 is A033507(n-1)
Column 5 is A033508(n-1)
Column 6 is A033509(n-1)
Column 7 is A033510(n-1) [and probably further sequences there]

Columns 1-7 have linear recurrences of order 2 3 6 9 20 36 72

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

```