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A251428 T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%I A251428 #10 Jul 23 2025 13:20:20
%S A251428 2,9,12,16,41,12,29,116,97,40,42,237,380,341,56,61,432,1113,1888,1003,
%T A251428 144,80,725,2532,6589,7458,3129,240,105,1128,5097,18952,34893,31980,
%U A251428 9439,544,130,1641,9120,44465,122452,183341,127566,28717,992,161,2316,15449
%N A251428 T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%C A251428 Table starts
%C A251428 ....2......9......16........29.........42.........61..........80..........105
%C A251428 ...12.....41.....116.......237........432........725........1128.........1641
%C A251428 ...12.....97.....380......1113.......2532.......5097........9120........15449
%C A251428 ...40....341....1888......6589......18952......44465.......94452.......180625
%C A251428 ...56...1003....7458.....34893.....122452.....349257......863840......1913597
%C A251428 ..144...3129...31980....183341.....791668....2647405.....7658288.....19250197
%C A251428 ..240...9439..127566....938895....4868362...19285211....64105154....183394583
%C A251428 ..544..28717..520568...4771117...29782800..137949185...526064608...1698285517
%C A251428 ..992..86695.2080650..24063611..179832500..976032575..4251906158..15488167451
%C A251428 .2112.261789.8370976.120999825.1084104408.6871688649.34199112972.140282803741
%H A251428 R. H. Hardin, <a href="/A251428/b251428.txt">Table of n, a(n) for n = 1..202</a>
%F A251428 Empirical for column k:
%F A251428 k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
%F A251428 k=2: [order 14]
%F A251428 k=3: [order 29]
%F A251428 Empirical for row n:
%F A251428 n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2
%F A251428 n=2: a(n) = a(n-1) +2*a(n-3) -a(n-4) -a(n-5) -a(n-6) -a(n-7) +2*a(n-8) +a(n-10) -a(n-11); also a polynomial of degree 3 plus a quasipolynomial of degree 1 with period 12
%F A251428 n=3: [order 38]
%e A251428 Some solutions for n=5 k=4
%e A251428 ..3....3....1....0....3....1....4....3....3....1....3....1....0....4....0....3
%e A251428 ..2....1....4....4....1....0....4....0....0....0....1....0....2....2....1....2
%e A251428 ..3....2....1....4....1....0....1....3....1....4....2....3....4....1....3....3
%e A251428 ..0....3....0....0....0....4....2....2....3....3....1....1....0....3....1....3
%e A251428 ..4....1....3....1....3....3....4....3....3....0....3....3....2....4....3....1
%e A251428 ..0....3....4....3....0....1....4....4....0....3....2....4....0....1....1....3
%e A251428 ..3....3....0....0....3....1....1....4....0....0....2....4....2....2....4....3
%Y A251428 Row 1 is A248434
%K A251428 nonn,tabl
%O A251428 1,1
%A A251428 _R. H. Hardin_, Dec 02 2014