cp's OEIS Frontend

A243607 T(n,k) = Number of length n+2 0..k arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..k introduced in 0..k order.

%I A243607 #6 Apr 17 2022 22:10:45
%S A243607 3,4,5,4,9,8,4,10,21,13,4,10,28,50,21,4,10,29,85,120,34,4,10,29,96,
%T A243607 269,289,55,4,10,29,97,349,870,697,89,4,10,29,97,365,1350,2844,1682,
%U A243607 144,4,10,29,97,366,1511,5425,9346,4060,233,4,10,29,97,366,1533,6726,22297,30792
%N A243607 T(n,k) = Number of length n+2 0..k arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..k introduced in 0..k order.
%C A243607 Table starts
%C A243607 ...3....4......4......4......4......4.......4.......4.......4.......4.......4
%C A243607 ...5....9.....10.....10.....10.....10......10......10......10......10......10
%C A243607 ...8...21.....28.....29.....29.....29......29......29......29......29......29
%C A243607 ..13...50.....85.....96.....97.....97......97......97......97......97......97
%C A243607 ..21..120....269....349....365....366.....366.....366.....366.....366.....366
%C A243607 ..34..289....870...1350...1511...1533....1534....1534....1534....1534....1534
%C A243607 ..55..697...2844...5425...6726...7020....7049....7050....7050....7050....7050
%C A243607 ..89.1682...9346..22297..31544..34631...35129...35166...35167...35167...35167
%C A243607 .144.4060..30792..92841.153328.181391..187993..188788..188834..188835..188835
%C A243607 .233.9801.101577.389456.763187.995139.1069914.1082913.1084123.1084179.1084180
%H A243607 R. H. Hardin, <a href="/A243607/b243607.txt">Table of n, a(n) for n = 1..9999</a>
%F A243607 Empirical for column k:
%F A243607 k=1: a(n) = a(n-1) +a(n-2),
%F A243607 k=2: a(n) = 3*a(n-1) -a(n-2) -a(n-3),
%F A243607 k=3: a(n) = 5*a(n-1) -5*a(n-2) -3*a(n-3) +3*a(n-4) +a(n-5),
%F A243607 k=4: a(n) = 8*a(n-1) -18*a(n-2) +5*a(n-3) +17*a(n-4) -4*a(n-5) -6*a(n-6) -a(n-7),
%F A243607 k=5: [order 9],
%F A243607 k=6: [order 11],
%F A243607 k=7: [order 13],
%F A243607 k=8: [order 15],
%F A243607 k=9: [order 17].
%e A243607 Some solutions for n=5, k=4
%e A243607 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243607 ..1....1....0....1....0....1....1....0....0....1....1....1....1....1....0....1
%e A243607 ..1....1....1....1....1....2....2....0....0....2....2....2....2....2....0....1
%e A243607 ..2....0....1....2....2....3....3....0....1....3....2....3....2....2....1....1
%e A243607 ..2....2....1....3....3....1....0....1....2....0....3....4....1....1....2....1
%e A243607 ..3....3....0....1....3....1....4....1....2....0....3....0....3....3....2....1
%e A243607 ..4....1....2....1....0....0....3....0....0....2....3....1....0....3....1....0
%Y A243607 Column 1 is A000045(n+3).
%Y A243607 Column 2 is A024537(n+1).
%K A243607 nonn,tabl
%O A243607 1,1
%A A243607 _R. H. Hardin_, Jun 07 2014