A303182 - OEIS

%I #6 May 25 2024 20:47:15

%S 1,2,2,4,8,4,8,17,25,8,16,37,31,81,16,32,78,72,135,264,32,64,169,170,

%T 297,547,857,64,128,361,382,931,1302,1938,2785,128,256,778,873,2569,

%U 5613,5050,6965,9050,256,512,1673,2013,6668,24751,29124,20188,25953,29407,512

%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1.....2.....4......8......16........32.........64.........128..........256

%C ...2.....8....17.....37......78.......169........361.........778.........1673

%C ...4....25....31.....72.....170.......382........873........2013.........4618

%C ...8....81...135....297.....931......2569.......6668.......17934........48674

%C ..16...264...547...1302....5613.....24751......88153......325770......1253442

%C ..32...857..1938...5050...29124....218980....1064399.....5463686.....31140302

%C ..64..2785..6965..20188..148501...1803435...11901719....82524101....673749714

%C .128..9050.25953..81926..786247..15559135..141429948..1341217380..15951682785

%C .256.29407.95602.329957.4126586.133939941.1665576584.21624053966.375045359077

%H R. H. Hardin, <a href="/A303182/b303182.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1).

%F k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4).

%F k=3: [order 13].

%F k=4: [order 31] for n>33.

%F k=5: [order 66] for n>73.

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1).

%F n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5) for n>6.

%F n=3: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -3*a(n-4) +a(n-5) for n>9.

%F n=4: [order 17] for n>22.

%F n=5: [order 34] for n>40.

%F n=6: [order 84] for n>90.

%e Some solutions for n=5, k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A240478.

%Y Row 1 is A000079(n-1).

%Y Row 2 is A281470.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 19 2018