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A268261
T(n,k)=Number of length-(n+1) 0..k arrays with new repeated values introduced in sequential order starting with zero.
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 29 2016
STATUS
approved