cp's OEIS Frontend

A269467 T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value.

%I A269467 #10 Nov 02 2024 09:13:26
%S A269467 2,3,4,4,9,6,5,16,24,10,6,25,60,66,14,7,36,120,228,174,22,8,49,210,
%T A269467 580,852,462,30,9,64,336,1230,2780,3180,1206,46,10,81,504,2310,7170,
%U A269467 13300,11796,3150,62,11,100,720,3976,15834,41730,63420,43644,8166,94,12,121
%N A269467 T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value.
%C A269467 Table starts
%C A269467 ..2.....3......4.......5........6.........7.........8..........9.........10
%C A269467 ..4.....9.....16......25.......36........49........64.........81........100
%C A269467 ..6....24.....60.....120......210.......336.......504........720........990
%C A269467 .10....66....228.....580.....1230......2310......3976.......6408.......9810
%C A269467 .14...174....852....2780.....7170.....15834.....31304......56952......97110
%C A269467 .22...462...3180...13300....41730....108402....246232.....505800.....960750
%C A269467 .30..1206..11796...63420...242370....741090...1934856....4488696....9499590
%C A269467 .46..3150..43644..301780..1405530...5060706..15190840...39808584...93880710
%C A269467 .62..8166.160980.1433180..8139570..34523202.119174216..352838520..927352710
%C A269467 .94.21150.592572.6795700.47082330.235304034.934305400.3125681352.9156504150
%C A269467 The conjectures regarding the recursions for column k are correct (see links) - _Sela Fried_, Oct 29 2024.
%H A269467 R. H. Hardin, <a href="/A269467/b269467.txt">Table of n, a(n) for n = 1..9999</a>
%H A269467 Sela Fried, <a href="https://arxiv.org/abs/2410.07237">Proofs of some Conjectures from the OEIS</a>, arXiv:2410.07237 [math.NT], 2024.
%F A269467 Empirical for column k:
%F A269467 k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
%F A269467 k=2: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3)
%F A269467 k=3: a(n) = 5*a(n-1) -18*a(n-3)
%F A269467 k=4: a(n) = 7*a(n-1) -4*a(n-2) -32*a(n-3)
%F A269467 k=5: a(n) = 9*a(n-1) -10*a(n-2) -50*a(n-3)
%F A269467 k=6: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3)
%F A269467 k=7: a(n) = 13*a(n-1) -28*a(n-2) -98*a(n-3)
%F A269467 Empirical for row n:
%F A269467 n=1: a(n) = n + 1
%F A269467 n=2: a(n) = n^2 + 2*n + 1
%F A269467 n=3: a(n) = n^3 + 3*n^2 + 2*n
%F A269467 n=4: a(n) = n^4 + 4*n^3 + 4*n^2 + n
%F A269467 n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 2*n^2 - n
%F A269467 n=6: a(n) = n^6 + 6*n^5 + 11*n^4 + 4*n^3 - n^2 + n
%F A269467 n=7: a(n) = n^7 + 7*n^6 + 16*n^5 + 8*n^4 - n^3 - n
%e A269467 Some solutions for n=6 k=4
%e A269467 ..2. .0. .3. .1. .1. .1. .2. .0. .1. .0. .3. .0. .3. .2. .4. .1
%e A269467 ..4. .3. .1. .1. .2. .0. .0. .2. .0. .2. .3. .1. .4. .0. .3. .4
%e A269467 ..3. .2. .0. .0. .0. .0. .2. .2. .1. .0. .4. .2. .4. .0. .4. .3
%e A269467 ..3. .0. .4. .2. .1. .1. .2. .1. .3. .4. .1. .4. .2. .4. .4. .1
%e A269467 ..1. .3. .4. .4. .0. .4. .4. .3. .4. .1. .4. .1. .2. .2. .0. .0
%e A269467 ..0. .1. .3. .3. .4. .3. .2. .4. .1. .3. .2. .2. .1. .4. .1. .2
%Y A269467 Column 1 is A027383.
%Y A269467 Row 1 is A000027(n+1).
%Y A269467 Row 2 is A000290(n+1).
%Y A269467 Row 3 is A007531(n+2).
%K A269467 nonn,tabl
%O A269467 1,1
%A A269467 _R. H. Hardin_, Feb 27 2016