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

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

R. H. Hardin, Table of n, a(n) for n = 1..221

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

Adjacent sequences: A251932 A251933 A251934 * A251936 A251937 A251938

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 11 2014

Status

approved