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%I #6 Dec 12 2014 21:03:12
%S 5,12,10,22,43,18,35,120,115,34,51,265,431,339,68,70,506,1191,1760,
%T 1047,136,92,875,2695,6293,7452,3185,268,117,1408,5340,17598,34186,
%U 30882,9614,528,145,2145,9615,41677,117980,180069,126098,28997,1048,176,3130,16098
%N T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus the median of adjacent triples multiplied by some arrangement of +-1 equal to zero
%C Table starts
%C ....5.....12......22........35.........51.........70..........92..........117
%C ...10.....43.....120.......265........506........875........1408.........2145
%C ...18....115.....431......1191.......2695.......5340........9615........16098
%C ...34....339....1760......6293......17598......41677.......87328.......166677
%C ...68...1047....7452.....34186.....117980.....334901......822796......1809610
%C ..136...3185...30882....180069.....759084....2556917.....7303048.....18382689
%C ..268...9614..126098....928891....4748562...18846528....62129347....177706943
%C ..528..28997..511108...4735071...29209810..135951349...514829238...1665351547
%C .1048..87432.2063052..23964561..177862134..968127101..4199965881..15321907453
%C .2088.263315.8301984.120719043.1076319648.6841930691.33956536010.139504731587
%H R. H. Hardin, <a href="/A251935/b251935.txt">Table of n, a(n) for n = 1..221</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -6*a(n-2) +6*a(n-3) -4*a(n-4)
%F k=2: [order 14] for n>17
%F Empirical for row n:
%F n=1: a(n) = (3/2)*n^2 + (5/2)*n + 1
%F n=2: a(n) = (1/6)*n^4 + (7/3)*n^3 + (23/6)*n^2 + (8/3)*n + 1
%F n=3: [linear recurrence of order 11; also a polynomial of degree 5 plus a quasipolynomial of degree 1 with period 6]
%F n=4: [linear recurrence order 18; also a polynomial of degree 5 plus a quasipolynomial of degree 2 with period 12]
%e Some solutions for n=5 k=4
%e ..2....4....3....0....2....1....4....2....0....2....0....2....2....4....2....3
%e ..0....1....4....4....4....1....0....3....4....1....3....4....0....3....1....2
%e ..3....1....4....1....3....4....0....1....1....4....4....2....4....3....1....4
%e ..2....4....2....0....4....1....2....2....2....0....3....3....4....4....2....3
%e ..3....3....4....0....1....2....1....0....2....1....3....2....3....3....4....4
%e ..4....3....2....2....4....0....1....0....1....0....2....1....2....3....3....4
%e ..2....1....1....3....2....3....3....1....0....2....0....1....4....2....1....4
%Y Row 1 is A000326(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 11 2014
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