A250361 T(n,k)=Number of length n arrays x(i), i=1..n with x(i) in i..i+k and no value appearing more than 3 times.

2, 3, 4, 4, 9, 8, 5, 16, 27, 16, 6, 25, 64, 81, 32, 7, 36, 125, 255, 243, 64, 8, 49, 216, 623, 1016, 729, 128, 9, 64, 343, 1293, 3094, 4048, 2187, 256, 10, 81, 512, 2397, 7712, 15365, 16128, 6561, 512, 11, 100, 729, 4091, 16700, 45866, 76300, 64257, 19683, 1024, 12

Offset: 1

Author

R. H. Hardin, Nov 19 2014

Keywords

• nonn
• tabl

Comments

Table starts

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

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

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

...16....81.....255.....623.....1293......2397.......4091.......6555.......9993

...32...243....1016....3094.....7712.....16700......32608......58826......99704

...64...729....4048...15365....45866....115963.....259106.....526505.....992530

..128..2187...16128...76300...272760....803382....2052904....4698744....9854280

..256..6561...64257..378880..1621963...5565230...16234706...41828450...97581710

..512.19683..256012.1881364..9644496..38548644..128373416..371780050..964209084

.1024.59049.1020000.9342081.57346376.266998350.1015004124.3304106808.9514922752

Examples

			Some solutions for n=6 k=4
..3....2....0....0....2....1....2....1....2....2....3....0....3....3....0....2
..2....3....1....4....4....4....3....3....1....3....2....3....1....3....4....4
..4....5....5....6....6....6....3....4....2....4....3....4....3....3....2....3
..3....3....4....3....5....6....7....4....5....3....6....7....4....5....6....7
..7....8....7....6....6....6....5....7....5....4....5....5....5....6....5....8
..5....7....9....9....9....9....8....5....9....5....9....7....7....6....9....5
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..447

Crossrefs

Column 1 is A000079

Column 2 is A000244

Column 3 is A206450

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Row 3 is A000578(n+1)

Cf. A248944, A250351

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

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

k=4: a(n) = 5*a(n-1) -2*a(n-4) -11*a(n-5) +a(n-8)

k=5: [order 13]

k=6: [order 25]

k=7: [order 56]

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = n^2 + 2*n + 1

n=3: a(n) = n^3 + 3*n^2 + 3*n + 1

n=4: a(n) = n^4 + 4*n^3 + 6*n^2 + 3*n + 3 for n>1

n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 5*n^2 + 17*n + 2 for n>2

n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 5*n^3 + 57*n^2 + 13*n + 1 for n>3

n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 147*n^3 + 49*n^2 + 7*n for n>4