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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 12
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 (list; table; graph; refs; listen; history; text; internal format)
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
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)
Sequence in context: A268457 A244940 A244832 * A269690 A269494 A269776
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 19 2014
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)