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

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....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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079

Column 2 is A076264(n)

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Cf. A248944

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).