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

1,1

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

Links

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

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

Example

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

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

Sequence in context: A224133 A228740 A269583 * A375379 A118263 A217478

Adjacent sequences: A250358 A250359 A250360 * A250362 A250363 A250364

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2014

Status

approved