A250351 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 2 times

2, 3, 4, 4, 9, 8, 5, 16, 26, 16, 6, 25, 62, 75, 32, 7, 36, 122, 235, 216, 64, 8, 49, 212, 581, 888, 622, 128, 9, 64, 338, 1221, 2724, 3349, 1791, 256, 10, 81, 506, 2287, 6900, 12734, 12620, 5157, 512, 11, 100, 722, 3935, 15186, 38543, 59406, 47545, 14849, 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....26.....62.....122......212.......338.......506........722........992

...16....75....235.....581.....1221......2287......3935.......6345.......9721

...32...216....888....2724.....6900.....15186.....30072......54888......93924

...64...622...3349...12734....38543.....99344....226247.....467642.....894599

..128..1791..12620...59406...214716....644040...1681860....3932472....8409252

..256..5157..47545..276816..1193739...4164930..12411486...32743710...78177402

..512.14849.179104.1289208..6628042..26882466..91384716..270990642..720784488

.1024.42756.674666.6002949.36773706.173276640.671639928.2238089580.6611373660

Links

R. H. Hardin, Table of n, a(n) for n = 1..418

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) -2*a(n-3) -5*a(n-4) +a(n-6) = A250346(n)

k=4: [order 12] = A250347(n)

k=5: [order 24] = A250348(n)

k=6: [order 48] = A250349(n).

k=7: [order 96] = A250350(n).

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 + 2*n + 2 = A250352(n).

n=4: a(n) = n^4 + 4*n^3 + 2*n^2 + 9*n + 1 for n>1 = A250353(n).

n=5: a(n) = n^5 + 5*n^4 + 25*n^2 + 5*n for n>2 = A250354(n).

n=6: a(n) = n^6 + 6*n^5 - 5*n^4 + 55*n^3 + 25*n^2 - 61*n + 98 for n>3 = A250355(n).

n=7: a(n) = n^7 + 7*n^6 - 14*n^5 + 105*n^4 + 105*n^3 - 532*n^2 + 1252*n - 744 for n>4 = A250356(n).

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A076264(n)

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Cf. A248944

Sequence in context: A268457 A244940 A244832 * A269690 A269494 A269776

Adjacent sequences: A250348 A250349 A250350 * A250352 A250353 A250354

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2014

Status

approved