login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 1,2,2,3,1,3,5,3,3,5,8,5,6,5,8,13,8,13,13,8,13,21,15,26,31,26,15,21,

%T 34,26,52,78,78,52,26,34,55,45,107,207,247,207,107,45,55,89,80,218,

%U 516,784,784,516,218,80,89,144,140,442,1288,2349,2905,2349,1288,442,140,144,233

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..1..2...3....5.....8.....13.....21......34.......55........89........144

%C ..2..1...3....5.....8.....15.....26......45.......80.......140........245

%C ..3..3...6...13....26.....52....107.....218......442.......899.......1829

%C ..5..5..13...31....78....207....516....1288.....3270......8271......20866

%C ..8..8..26...78...247....784...2349....7191....22268.....68384.....210050

%C .13.15..52..207...784...2905..10496...38721...144148....531780....1960675

%C .21.26.107..516..2349..10496..46165..208159...942764...4213744...18870716

%C .34.45.218.1288..7191..38721.208159.1143583..6263377..33963639..184912113

%C .55.80.442.3270.22268.144148.942764.6263377.41368803.271753441.1792754281

%H R. H. Hardin, <a href="/A318545/b318545.txt">Table of n, a(n) for n = 1..924</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +3*a(n-3) +a(n-4) +3*a(n-5) +a(n-7) for n>8

%F k=4: [order 13] for n>14

%F k=5: [order 23] for n>24

%F k=6: [order 37] for n>38

%F k=7: [order 63] for n>64

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A193147.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 28 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)