A269776 - OEIS

%I #4 Mar 04 2016 14:42:31

%S 2,3,4,4,9,8,5,16,27,14,6,25,64,78,24,7,36,125,252,222,40,8,49,216,

%T 620,984,624,66,9,64,343,1290,3060,3816,1740,108,10,81,512,2394,7680,

%U 15040,14724,4824,176,11,100,729,4088,16674,45600,73680,56592,13320,286,12,121

%N T(n,k)=Number of length-n 0..k arrays with every repeated value unequal to the previous repeated value plus one mod k+1.

%C Table starts

%C ...2.....3......4.......5........6.........7..........8..........9.........10

%C ...4.....9.....16......25.......36........49.........64.........81........100

%C ...8....27.....64.....125......216.......343........512........729.......1000

%C ..14....78....252.....620.....1290......2394.......4088.......6552.......9990

%C ..24...222....984....3060.....7680.....16674......32592......58824......99720

%C ..40...624...3816...15040....45600....115920.....259504.....527616.....994680

%C ..66..1740..14724...73680...270150....804636....2063880....4728384....9915210

%C .108..4824..56592..360000..1597500...5577768...16398144...42342912...98779500

%C .176.13320.216864.1755200..9432000..38621016..130175360..378929664..983566800

%C .286.36672.829116.8542720.55616250.267152256.1032602872.3389054976.9788946390

%H R. H. Hardin, <a href="/A269776/b269776.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for column k (apparently a(n) = 2*k*a(n-1) -k*(k-1)*a(n-2) -k^2*a(n-3)):

%F k=1: a(n) = 2*a(n-1) -a(n-3)

%F k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3)

%F k=3: a(n) = 6*a(n-1) -6*a(n-2) -9*a(n-3)

%F k=4: a(n) = 8*a(n-1) -12*a(n-2) -16*a(n-3)

%F k=5: a(n) = 10*a(n-1) -20*a(n-2) -25*a(n-3)

%F k=6: a(n) = 12*a(n-1) -30*a(n-2) -36*a(n-3)

%F k=7: a(n) = 14*a(n-1) -42*a(n-2) -49*a(n-3)

%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 + 3*n + 1

%F n=4: a(n) = n^4 + 4*n^3 + 6*n^2 + 3*n

%F n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 7*n^2 + n

%F n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 4*n^2

%F n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 25*n^4 + 11*n^3 + n^2

%e Some solutions for n=6 k=4

%e ..1. .4. .0. .3. .3. .4. .0. .4. .0. .0. .2. .0. .2. .4. .1. .0

%e ..4. .0. .3. .0. .0. .0. .4. .4. .4. .0. .0. .3. .2. .3. .2. .4

%e ..3. .1. .4. .3. .2. .0. .3. .2. .0. .3. .3. .4. .4. .1. .3. .0

%e ..2. .2. .4. .0. .2. .4. .3. .0. .2. .3. .1. .1. .1. .1. .1. .4

%e ..1. .4. .4. .3. .3. .0. .1. .3. .0. .0. .1. .3. .0. .4. .3. .0

%e ..2. .1. .1. .2. .4. .0. .1. .3. .1. .4. .1. .2. .3. .4. .3. .4

%Y Column 1 is A019274(n+2).

%Y Column 2 is A269613.

%Y Row 1 is A000027(n+1).

%Y Row 2 is A000290(n+1).

%Y Row 3 is A000578(n+1).

%Y Row 4 is A058895(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 04 2016