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A267232
T(n,k)=Number of length-n 0..k arrays with no following elements greater than or equal to the first repeated value.
12
2, 3, 4, 4, 9, 5, 5, 16, 21, 6, 6, 25, 54, 47, 7, 7, 36, 110, 176, 103, 8, 8, 49, 195, 470, 564, 223, 9, 9, 64, 315, 1030, 1980, 1790, 479, 10, 10, 81, 476, 1981, 5375, 8274, 5646, 1023, 11, 11, 100, 684, 3472, 12327, 27854, 34396, 17732, 2175, 12, 12, 121, 945, 5676
OFFSET
1,1
COMMENTS
Table starts
..2....3......4.......5........6.........7.........8..........9.........10
..4....9.....16......25.......36........49........64.........81........100
..5...21.....54.....110......195.......315.......476........684........945
..6...47....176.....470.....1030......1981......3472.......5676.......8790
..7..103....564....1980.....5375.....12327.....25088......46704......81135
..8..223...1790....8274....27854.....76237....180292.....382404.....745548
..9..479...5646...34396...143695....469623...1291052....3121008....6830757
.10.1023..17732..142474...738990...2884909...9222184...25415028...62455218
.11.2175..55512..588596..3791775..17686215..65755592..206617680..570177387
.12.4607.173354.2426738.19421854.108259885.468196540.1677626052.5199327816
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) for n>3
k=2: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>4
k=3: a(n) = 9*a(n-1) -29*a(n-2) +39*a(n-3) -18*a(n-4) for n>5
k=4: a(n) = 14*a(n-1) -75*a(n-2) +190*a(n-3) -224*a(n-4) +96*a(n-5) for n>6
k=5: [order 6] for n>7
k=6: [order 7] for n>8
k=7: [order 8] for n>9
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 + (5/2)*n^2 + (3/2)*n
n=4: a(n) = n^4 + (17/6)*n^3 + 2*n^2 + (1/6)*n
n=5: a(n) = n^5 + (37/12)*n^4 + (5/2)*n^3 + (5/12)*n^2
n=6: a(n) = n^6 + (197/60)*n^5 + 3*n^4 + (3/4)*n^3 - (1/30)*n
n=7: a(n) = n^7 + (69/20)*n^6 + (7/2)*n^5 + (7/6)*n^4 - (7/60)*n^2
EXAMPLE
Some solutions for n=6 k=4
..3....3....1....0....4....0....3....2....4....2....4....4....4....1....0....1
..1....4....4....2....4....2....1....0....3....3....2....3....1....4....1....2
..0....2....4....0....2....0....0....3....4....2....1....0....0....3....3....0
..2....0....3....4....2....3....1....2....4....2....2....1....3....2....0....2
..4....2....1....0....1....1....4....3....1....1....0....4....0....1....3....0
..4....1....0....4....2....2....4....2....0....1....2....4....2....4....2....3
CROSSREFS
Column 1 is A000027(n+2).
Row 1 is A000027(n+1).
Row 2 is A000290(n+1).
Row 3 is A160378(n+1).
Sequence in context: A241037 A097093 A056877 * A269606 A269640 A269409
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 12 2016
STATUS
approved