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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.

%I A267232 #4 Jan 12 2016 08:18:57
%S A267232 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,
%T A267232 564,223,9,9,64,315,1030,1980,1790,479,10,10,81,476,1981,5375,8274,
%U A267232 5646,1023,11,11,100,684,3472,12327,27854,34396,17732,2175,12,12,121,945,5676
%N A267232 T(n,k)=Number of length-n 0..k arrays with no following elements greater than or equal to the first repeated value.
%C A267232 Table starts
%C A267232 ..2....3......4.......5........6.........7.........8..........9.........10
%C A267232 ..4....9.....16......25.......36........49........64.........81........100
%C A267232 ..5...21.....54.....110......195.......315.......476........684........945
%C A267232 ..6...47....176.....470.....1030......1981......3472.......5676.......8790
%C A267232 ..7..103....564....1980.....5375.....12327.....25088......46704......81135
%C A267232 ..8..223...1790....8274....27854.....76237....180292.....382404.....745548
%C A267232 ..9..479...5646...34396...143695....469623...1291052....3121008....6830757
%C A267232 .10.1023..17732..142474...738990...2884909...9222184...25415028...62455218
%C A267232 .11.2175..55512..588596..3791775..17686215..65755592..206617680..570177387
%C A267232 .12.4607.173354.2426738.19421854.108259885.468196540.1677626052.5199327816
%H A267232 R. H. Hardin, <a href="/A267232/b267232.txt">Table of n, a(n) for n = 1..9999</a>
%F A267232 Empirical for column k:
%F A267232 k=1: a(n) = 2*a(n-1) -a(n-2) for n>3
%F A267232 k=2: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>4
%F A267232 k=3: a(n) = 9*a(n-1) -29*a(n-2) +39*a(n-3) -18*a(n-4) for n>5
%F A267232 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
%F A267232 k=5: [order 6] for n>7
%F A267232 k=6: [order 7] for n>8
%F A267232 k=7: [order 8] for n>9
%F A267232 Empirical for row n:
%F A267232 n=1: a(n) = n + 1
%F A267232 n=2: a(n) = n^2 + 2*n + 1
%F A267232 n=3: a(n) = n^3 + (5/2)*n^2 + (3/2)*n
%F A267232 n=4: a(n) = n^4 + (17/6)*n^3 + 2*n^2 + (1/6)*n
%F A267232 n=5: a(n) = n^5 + (37/12)*n^4 + (5/2)*n^3 + (5/12)*n^2
%F A267232 n=6: a(n) = n^6 + (197/60)*n^5 + 3*n^4 + (3/4)*n^3 - (1/30)*n
%F A267232 n=7: a(n) = n^7 + (69/20)*n^6 + (7/2)*n^5 + (7/6)*n^4 - (7/60)*n^2
%e A267232 Some solutions for n=6 k=4
%e A267232 ..3....3....1....0....4....0....3....2....4....2....4....4....4....1....0....1
%e A267232 ..1....4....4....2....4....2....1....0....3....3....2....3....1....4....1....2
%e A267232 ..0....2....4....0....2....0....0....3....4....2....1....0....0....3....3....0
%e A267232 ..2....0....3....4....2....3....1....2....4....2....2....1....3....2....0....2
%e A267232 ..4....2....1....0....1....1....4....3....1....1....0....4....0....1....3....0
%e A267232 ..4....1....0....4....2....2....4....2....0....1....2....4....2....4....2....3
%Y A267232 Column 1 is A000027(n+2).
%Y A267232 Row 1 is A000027(n+1).
%Y A267232 Row 2 is A000290(n+1).
%Y A267232 Row 3 is A160378(n+1).
%K A267232 nonn,tabl
%O A267232 1,1
%A A267232 _R. H. Hardin_, Jan 12 2016