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A269409 T(n,k)=Number of length-n 0..k arrays with no repeated value greater than or equal to the previous repeated value.

%I A269409 #4 Feb 25 2016 14:38:54
%S A269409 2,3,4,4,9,6,5,16,24,9,6,25,60,63,12,7,36,120,222,159,16,8,49,210,570,
%T A269409 804,394,20,9,64,336,1215,2670,2872,957,25,10,81,504,2289,6960,12380,
%U A269409 10132,2292,30,11,100,720,3948,15477,39560,56890,35383,5419,36,12,121
%N A269409 T(n,k)=Number of length-n 0..k arrays with no repeated value greater than or equal to the previous repeated value.
%C A269409 Table starts
%C A269409 ..2.....3......4.......5........6.........7.........8..........9.........10
%C A269409 ..4.....9.....16......25.......36........49........64.........81........100
%C A269409 ..6....24.....60.....120......210.......336.......504........720........990
%C A269409 ..9....63....222.....570.....1215......2289......3948.......6372.......9765
%C A269409 .12...159....804....2670.....6960.....15477.....30744......56124......95940
%C A269409 .16...394...2872...12380....39560....104006....238224.....492312.....939360
%C A269409 .20...957..10132...56890...223320....695135...1837752....4302612....9168780
%C A269409 .25..2292..35383..259445..1253190...4623815..14121282...37478718...89241015
%C A269409 .30..5419.122480.1175355..6995660..30625210.108123624..325487010..866361210
%C A269409 .36.12678.420752.5293671.38870136.202067047.825227424.2819002698.8390905692
%H A269409 R. H. Hardin, <a href="/A269409/b269409.txt">Table of n, a(n) for n = 1..9999</a>
%F A269409 Empirical for column k:
%F A269409 k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
%F A269409 k=2: a(n) = 6*a(n-1) -9*a(n-2) -8*a(n-3) +24*a(n-4) -16*a(n-6)
%F A269409 k=3: [order 8]
%F A269409 k=4: [order 10]
%F A269409 k=5: [order 12]
%F A269409 k=6: [order 14]
%F A269409 k=7: [order 16]
%F A269409 Empirical for row n:
%F A269409 n=1: a(n) = n + 1
%F A269409 n=2: a(n) = n^2 + 2*n + 1
%F A269409 n=3: a(n) = n^3 + 3*n^2 + 2*n
%F A269409 n=4: a(n) = n^4 + 4*n^3 + (7/2)*n^2 + (1/2)*n
%F A269409 n=5: a(n) = n^5 + 5*n^4 + (11/2)*n^3 + n^2 - (1/2)*n
%F A269409 n=6: a(n) = n^6 + 6*n^5 + 8*n^4 + (5/3)*n^3 - n^2 + (1/3)*n
%F A269409 n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + (8/3)*n^4 - (11/6)*n^3 + (1/3)*n^2 - (1/6)*n
%e A269409 Some solutions for n=6 k=4
%e A269409 ..3. .2. .1. .0. .1. .3. .1. .0. .0. .1. .0. .2. .4. .3. .0. .4
%e A269409 ..3. .0. .0. .3. .3. .4. .4. .2. .3. .4. .4. .4. .2. .4. .4. .4
%e A269409 ..1. .3. .1. .0. .3. .4. .2. .4. .1. .1. .0. .2. .0. .2. .2. .2
%e A269409 ..0. .4. .4. .3. .0. .0. .1. .0. .2. .4. .2. .4. .2. .4. .1. .4
%e A269409 ..2. .0. .0. .2. .3. .0. .2. .4. .3. .2. .0. .0. .4. .1. .1. .2
%e A269409 ..1. .0. .1. .4. .4. .4. .3. .4. .4. .3. .2. .0. .0. .3. .2. .4
%Y A269409 Column 1 is A002620(n+2).
%Y A269409 Column 2 is A267960.
%Y A269409 Column 3 is A267928.
%Y A269409 Diagonal is A268205.
%Y A269409 Row 1 is A000027(n+1).
%Y A269409 Row 2 is A000290(n+1).
%Y A269409 Row 3 is A007531(n+2).
%K A269409 nonn,tabl
%O A269409 1,1
%A A269409 _R. H. Hardin_, Feb 25 2016