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%I #4 Jan 15 2016 15:27:42
%S 2,3,4,4,9,7,5,16,24,12,6,25,58,62,21,7,36,115,204,160,38,8,49,201,
%T 515,712,418,71,9,64,322,1096,2285,2490,1112,136,10,81,484,2072,5921,
%U 10119,8770,3018,265,11,100,693,3592,13216,31880,44901,31200,8352,522,12,121
%N T(n,k)=Number of length-n 0..k arrays with no following elements larger than the first repeated value.
%C Table starts
%C ...2.....3......4.......5........6.........7.........8..........9.........10
%C ...4.....9.....16......25.......36........49........64.........81........100
%C ...7....24.....58.....115......201.......322.......484........693........955
%C ..12....62....204.....515.....1096......2072......3592.......5829.......8980
%C ..21...160....712....2285.....5921.....13216.....26440......48657......83845
%C ..38...418...2490...10119....31880.....83972....193852.....404589.....779938
%C ..71..1112...8770...44901...171601....532840...1418740....3357537....7240267
%C .136..3018..31200..200119...925176...3381860..10378144...27838701...67140808
%C .265..8352.112300..897301..5002641..21491464..75944464..230790033..622347697
%C .522.23522.409254.4052183.27155800.136856180.556295860.1914051597.5768860606
%H R. H. Hardin, <a href="/A267471/b267471.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)
%F k=2: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4)
%F k=3: a(n) = 13*a(n-1) -65*a(n-2) +155*a(n-3) -174*a(n-4) +72*a(n-5)
%F k=4: a(n) = 19*a(n-1) -145*a(n-2) +565*a(n-3) -1174*a(n-4) +1216*a(n-5) -480*a(n-6)
%F k=5: [order 7]
%F k=6: [order 8]
%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 + (5/2)*n^2 + (5/2)*n + 1
%F n=4: a(n) = n^4 + (17/6)*n^3 + 4*n^2 + (19/6)*n + 1
%F n=5: a(n) = n^5 + (37/12)*n^4 + (11/2)*n^3 + (77/12)*n^2 + 4*n + 1
%F n=6: a(n) = n^6 + (197/60)*n^5 + 7*n^4 + (43/4)*n^3 + 10*n^2 + (149/30)*n + 1
%F n=7: a(n) = n^7 + (69/20)*n^6 + (17/2)*n^5 + (97/6)*n^4 + 20*n^3 + (893/60)*n^2 + 6*n + 1
%e Some solutions for n=6 k=4
%e ..0....1....1....4....0....1....0....4....1....2....3....4....4....1....0....3
%e ..4....0....4....0....4....0....3....0....2....3....1....4....3....4....1....0
%e ..4....2....2....4....3....4....2....4....0....0....2....4....2....0....3....2
%e ..0....3....4....0....3....4....3....3....1....1....4....2....4....4....4....3
%e ..2....4....1....1....0....0....1....1....2....1....3....1....3....2....1....3
%e ..4....4....1....1....3....2....0....2....0....0....0....1....4....3....1....1
%Y Column 1 is A005126(n-1).
%Y Row 1 is A000027(n+1).
%Y Row 2 is A000290(n+1).
%Y Row 3 is A081436.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 15 2016
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