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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 (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 ..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 R. H. Hardin, Table of n, a(n) for n = 1..9999 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 Adjacent sequences:  A267229 A267230 A267231 * A267233 A267234 A267235 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 12 2016 STATUS approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)