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A249707 T(n,k)=Number of length n+3 0..k arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

%I A249707 #6 Jul 23 2025 12:06:25
%S A249707 10,39,14,100,69,20,205,208,125,28,366,485,440,221,38,595,966,1153,
%T A249707 896,377,52,904,1729,2524,2601,1724,659,72,1305,2864,4893,6172,5425,
%U A249707 3440,1177,100,1810,4473,8688,12789,13666,11925,7056,2119,138,2431,6670,14433
%N A249707 T(n,k)=Number of length n+3 0..k arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.
%C A249707 Table starts
%C A249707 ..10...39...100....205.....366.....595.....904.....1305.....1810.....2431
%C A249707 ..14...69...208....485.....966....1729....2864.....4473.....6670.....9581
%C A249707 ..20..125...440...1153....2524....4893....8688....14433....22756....34397
%C A249707 ..28..221...896...2601....6172...12789...24032....41937....69052...108493
%C A249707 ..38..377..1724...5425...13666...29673...57912...104289...176350...283481
%C A249707 ..52..659..3440..11925...32500...75495..156416...297321...528340...889339
%C A249707 ..72.1177..7056..27113...80360..200489..442144...888465..1659976..2924889
%C A249707 .100.2119.14544..61725..198164..528755.1235840..2613945..5113060..9391327
%C A249707 .138.3805.29620.137593..474302.1341901.3295784..7275729.14775346.28054653
%C A249707 .190.6857.60416.307437.1140694.3434085.8902160.20616873.43717054.86348977
%H A249707 R. H. Hardin, <a href="/A249707/b249707.txt">Table of n, a(n) for n = 1..8549</a>
%F A249707 Empirical for column k:
%F A249707 k=1: a(n) = a(n-1) +a(n-4)
%F A249707 k=2: [order 10]
%F A249707 k=3: [order 17]
%F A249707 k=4: [order 24]
%F A249707 k=5: [order 30]
%F A249707 k=6: [order 37]
%F A249707 k=7: [order 43]
%F A249707 Empirical for row n:
%F A249707 n=1: a(n) = 2*n^3 + 4*n^2 + 3*n + 1
%F A249707 n=2: a(n) = (1/2)*n^4 + 4*n^3 + (11/2)*n^2 + 3*n + 1
%F A249707 n=3: a(n) = (1/15)*n^5 + 2*n^4 + 7*n^3 + 7*n^2 + (44/15)*n + 1
%F A249707 n=4: a(n) = (7/15)*n^5 + 5*n^4 + 11*n^3 + 8*n^2 + (38/15)*n + 1
%F A249707 n=5: a(n) = (5/3)*n^5 + 10*n^4 + 16*n^3 + 8*n^2 + (4/3)*n + 1
%F A249707 n=6: a(n) = (1/5)*n^6 + (73/15)*n^5 + 18*n^4 + 22*n^3 + (34/5)*n^2 - (13/15)*n + 1
%F A249707 n=7: a(n) = (1/70)*n^7 + (19/15)*n^6 + (178/15)*n^5 + 30*n^4 + (851/30)*n^3 + (56/15)*n^2 - (446/105)*n + 1
%e A249707 Some solutions for n=6 k=4
%e A249707 ..3....3....2....4....1....4....3....4....3....1....0....3....3....2....3....2
%e A249707 ..1....3....4....1....4....2....3....1....4....1....2....0....3....1....3....1
%e A249707 ..0....3....0....1....1....0....2....1....3....2....2....0....3....1....4....2
%e A249707 ..1....2....2....1....1....2....4....1....0....1....3....0....4....0....0....4
%e A249707 ..1....4....2....4....0....4....3....2....3....1....2....0....2....1....3....2
%e A249707 ..1....3....2....1....3....2....3....1....3....1....1....0....3....3....3....1
%e A249707 ..0....3....0....1....1....1....3....1....3....3....2....0....3....1....4....2
%e A249707 ..4....3....4....1....1....2....2....1....1....1....3....0....4....1....3....4
%e A249707 ..1....0....2....0....0....2....3....4....4....0....2....1....1....0....2....2
%Y A249707 Column 1 is A246473
%Y A249707 Row 1 is A059722(n+1)
%K A249707 nonn,tabl
%O A249707 1,1
%A A249707 _R. H. Hardin_, Nov 04 2014