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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000051.

Row 1 is A002061(n+1).

Row 2 is A100705.

Sequence in context: A065175 A065283 A352670 * A090940 A090916 A342701

Adjacent sequences: A268258 A268259 A268260 * A268262 A268263 A268264

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 29 2016

Status

approved