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A251935
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
14
5, 12, 10, 22, 43, 18, 35, 120, 115, 34, 51, 265, 431, 339, 68, 70, 506, 1191, 1760, 1047, 136, 92, 875, 2695, 6293, 7452, 3185, 268, 117, 1408, 5340, 17598, 34186, 30882, 9614, 528, 145, 2145, 9615, 41677, 117980, 180069, 126098, 28997, 1048, 176, 3130, 16098
OFFSET
1,1
COMMENTS
Table starts
....5.....12......22........35.........51.........70..........92..........117
...10.....43.....120.......265........506........875........1408.........2145
...18....115.....431......1191.......2695.......5340........9615........16098
...34....339....1760......6293......17598......41677.......87328.......166677
...68...1047....7452.....34186.....117980.....334901......822796......1809610
..136...3185...30882....180069.....759084....2556917.....7303048.....18382689
..268...9614..126098....928891....4748562...18846528....62129347....177706943
..528..28997..511108...4735071...29209810..135951349...514829238...1665351547
.1048..87432.2063052..23964561..177862134..968127101..4199965881..15321907453
.2088.263315.8301984.120719043.1076319648.6841930691.33956536010.139504731587
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -6*a(n-2) +6*a(n-3) -4*a(n-4)
k=2: [order 14] for n>17
Empirical for row n:
n=1: a(n) = (3/2)*n^2 + (5/2)*n + 1
n=2: a(n) = (1/6)*n^4 + (7/3)*n^3 + (23/6)*n^2 + (8/3)*n + 1
n=3: [linear recurrence of order 11; also a polynomial of degree 5 plus a quasipolynomial of degree 1 with period 6]
n=4: [linear recurrence order 18; also a polynomial of degree 5 plus a quasipolynomial of degree 2 with period 12]
EXAMPLE
Some solutions for n=5 k=4
..2....4....3....0....2....1....4....2....0....2....0....2....2....4....2....3
..0....1....4....4....4....1....0....3....4....1....3....4....0....3....1....2
..3....1....4....1....3....4....0....1....1....4....4....2....4....3....1....4
..2....4....2....0....4....1....2....2....2....0....3....3....4....4....2....3
..3....3....4....0....1....2....1....0....2....1....3....2....3....3....4....4
..4....3....2....2....4....0....1....0....1....0....2....1....2....3....3....4
..2....1....1....3....2....3....3....1....0....2....0....1....4....2....1....4
CROSSREFS
Row 1 is A000326(n+1)
Sequence in context: A066326 A015242 A009415 * A195031 A265028 A259911
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 11 2014
STATUS
approved