A268261 T(n,k)=Number of length-(n+1) 0..k arrays with new repeated values introduced in sequential order starting with zero.

3, 7, 5, 13, 17, 9, 21, 43, 42, 17, 31, 89, 143, 106, 33, 43, 161, 378, 479, 273, 65, 57, 265, 837, 1610, 1616, 717, 129, 73, 407, 1634, 4357, 6877, 5492, 1918, 257, 91, 593, 2907, 10082, 22710, 29461, 18804, 5218, 513, 111, 829, 4818, 20771, 62249, 118530, 126591

Offset: 1

Author

R. H. Hardin, Jan 29 2016

Keywords

• nonn
• tabl

Comments

Table starts

....3.....7.....13.......21.......31........43.........57..........73

....5....17.....43.......89......161.......265........407.........593

....9....42....143......378......837......1634.......2907........4818

...17...106....479.....1610.....4357.....10082......20771.......39154

...33...273...1616.....6877....22710.....62249.....148468......318261

...65...717...5492....29461...118530....384605....1061632.....2587557

..129..1918..18804...126591...619490...2377935....7594224....21042479

..257..5218..64869...545627..3242265..14712729...54345509...171161319

..513.14413.225483..2359152.16993552..91096234..389060724..1392571084

.1025.40349.789747.10233188.89197862.564452368.2786424182.11332701236

Examples

			Some solutions for n=5 k=4
..0....4....1....2....0....3....2....1....0....1....4....1....1....1....3....2
..0....3....4....4....0....2....4....0....3....4....0....3....0....2....4....0
..4....4....0....0....4....3....3....0....2....1....4....4....4....3....0....0
..3....0....2....0....0....4....4....4....0....4....1....0....3....2....3....4
..1....0....3....1....2....0....1....3....3....0....0....3....1....3....0....3
..3....3....2....4....0....0....4....0....2....3....3....1....3....0....4....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9999

Crossrefs

Column 1 is A000051.

Row 1 is A002061(n+1).

Row 2 is A100705.

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -15*a(n-2) +7*a(n-3) +6*a(n-4)

k=3: a(n) = 13*a(n-1) -60*a(n-2) +105*a(n-3) -11*a(n-4) -94*a(n-5) -24*a(n-6)

k=4: [order 8]

k=5: [order 10]

k=6: [order 12]

k=7: [order 14]

Empirical for row n:

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

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

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

n=4: a(n) = n^5 + n^4 + 4*n^3 + 3*n^2 + 6*n + 2

n=5: a(n) = n^6 + n^5 + 5*n^4 + 4*n^3 + 12*n^2 + 6*n + 5 for n>1

n=6: a(n) = n^7 + n^6 + 6*n^5 + 5*n^4 + 20*n^3 + 12*n^2 + 20*n + 5 for n>1

n=7: a(n) = n^8 + n^7 + 7*n^6 + 6*n^5 + 30*n^4 + 20*n^3 + 50*n^2 + 20*n + 15 for n>2