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 A318068 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8

%I #4 Aug 15 2018 13:13:18

%S 0,1,1,1,5,1,2,18,18,2,3,67,98,67,3,5,249,649,649,249,5,8,925,4003,

%T 7170,4003,925,8,13,3437,25106,76927,76927,25106,3437,13,21,12770,

%U 156846,829137,1405892,829137,156846,12770,21,34,47447,980960,8929364,25994502

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1.......1..........2............3..............5................8

%C ..1.....5......18.........67..........249............925.............3437

%C ..1....18......98........649.........4003..........25106...........156846

%C ..2....67.....649.......7170........76927.........829137..........8929364

%C ..3...249....4003......76927......1405892.......25994502........479322719

%C ..5...925...25106.....829137.....25994502......824452611......26085599617

%C ..8..3437..156846....8929364....479322719....26085599617....1415459855958

%C .13.12770..980960...96178466...8844178475...825766558967...76853282341918

%C .21.47447.6133497.1035919809.163160290206.26137612655323.4172233315256556

%H R. H. Hardin, <a href="/A318068/b318068.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

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

%F k=3: [order 11] for n>12

%F k=4: [order 39]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 15 2018

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Last modified September 23 10:17 EDT 2023. Contains 365544 sequences. (Running on oeis4.)