|
%I #4 Mar 01 2016 12:43:12
%S 2,3,4,4,9,6,5,16,24,8,6,25,60,62,10,7,36,120,222,154,12,8,49,210,572,
%T 804,376,14,9,64,336,1220,2692,2878,902,16,10,81,504,2298,7030,12570,
%U 10192,2142,18,11,100,720,3962,15630,40288,58280,35812,5040,20,12,121
%N T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one or less.
%C Table starts
%C ..2.....3......4.......5........6.........7.........8..........9.........10
%C ..4.....9.....16......25.......36........49........64.........81........100
%C ..6....24.....60.....120......210.......336.......504........720........990
%C ..8....62....222.....572.....1220......2298......3962.......6392.......9792
%C .10...154....804....2692.....7030.....15630.....31024......56584......96642
%C .12...376...2878...12570....40288....105892....242226.....499798.....952180
%C .14...902..10192...58280...229754....714874...1886252....4405772....9366790
%C .16..2142..35812..268704..1304934...4811578..14654952...38768412...92013754
%C .18..5040.125012.1233046..7385898..32300252.113629480..340600002..902743646
%C .20.11786.434110.5636046.41679780.216337084.879470154.2988094770.8846649136
%H R. H. Hardin, <a href="/A269606/b269606.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2)
%F k=2: a(n) = 5*a(n-1) -5*a(n-2) -8*a(n-3) +12*a(n-4)
%F k=3: a(n) = 7*a(n-1) -9*a(n-2) -23*a(n-3) +31*a(n-4) +33*a(n-5)
%F k=4: [order 7]
%F k=5: [order 7]
%F k=6: [order 9]
%F k=7: [order 9]
%F Empirical for row n:
%F n=1: a(n) = n + 1
%F n=2: a(n) = n^2 + 2*n + 1
%F n=3: a(n) = n^3 + 3*n^2 + 2*n
%F n=4: a(n) = n^4 + 4*n^3 + 4*n^2 - n
%F n=5: a(n) = n^5 + 5*n^4 + 7*n^3 - 4*n^2 + n
%F n=6: a(n) = n^6 + 6*n^5 + 11*n^4 - 8*n^3 + n^2 + 3*n - 2
%F n=7: a(n) = n^7 + 7*n^6 + 16*n^5 - 12*n^4 - 5*n^3 + 18*n^2 - 15*n + 4
%e Some solutions for n=6 k=4
%e ..1. .0. .3. .0. .3. .2. .1. .1. .0. .3. .2. .3. .2. .1. .1. .2
%e ..3. .2. .2. .2. .0. .4. .2. .2. .3. .4. .0. .0. .0. .4. .1. .2
%e ..0. .0. .3. .4. .3. .2. .3. .3. .1. .4. .4. .3. .3. .3. .2. .3
%e ..4. .1. .0. .3. .1. .0. .3. .1. .0. .3. .1. .1. .3. .0. .1. .1
%e ..3. .3. .2. .4. .3. .4. .0. .0. .1. .4. .2. .3. .2. .3. .2. .0
%e ..1. .3. .1. .3. .0. .4. .1. .3. .1. .0. .3. .3. .0. .3. .0. .0
%Y Column 1 is A004275(n+1).
%Y Column 3 is A269532.
%Y Row 1 is A000027(n+1).
%Y Row 2 is A000290(n+1).
%Y Row 3 is A007531(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 01 2016
| 