A252177 T(n,k)=Number of length n+2 0..k arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero

2, 3, 12, 4, 49, 12, 5, 132, 83, 40, 6, 285, 264, 369, 56, 7, 536, 687, 1872, 957, 144, 8, 917, 1428, 6361, 6820, 3217, 240, 9, 1464, 2729, 17092, 30315, 31420, 9295, 544, 10, 2217, 4680, 39109, 100894, 179225, 123826, 28977, 992, 11, 3220, 7661, 79672

Offset

1,1

Comments

Table starts

....2......3.......4.........5..........6..........7...........8............9

...12.....49.....132.......285........536........917........1464.........2217

...12.....83.....264.......687.......1428.......2729........4680.........7661

...40....369....1872......6361......17092......39109.......79672.......148673

...56....957....6820.....30315.....100894.....277101......654644......1397115

..144...3217...31420....179225.....753200....2485637.....6994984.....17238485

..240...9295..123826....907249....4652710...18231947....59838132....169267931

..544..28977..515268...4728833...29364176..135424961...513937352...1653595049

..992..86267.2058802..23847033..177955614..963247737..4190189694..15244143115

.2112.262541.8332796.120644221.1080135428.6838373877.34020988396.139530739057

Links

R. H. Hardin, Table of n, a(n) for n = 1..181

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)

k=2: [order 14]

k=3: [order 39] for n>40

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = (1/6)*n^4 + (7/3)*n^3 + (29/6)*n^2 + (11/3)*n + 1

n=3: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9); also a polynomial of degree 5 plus a quasipolynomial of degree 2 with period 2

n=4: [linear recurrence of order 23; also a polynomial of degree 6 plus a quasipolynomial of degree 3 with period 12]

Example

Some solutions for n=5 k=4
..0....0....2....1....1....1....1....3....3....2....2....2....1....3....0....4
..3....2....1....2....0....1....0....4....4....3....2....2....3....0....2....2
..3....3....4....3....2....2....1....1....4....3....3....4....2....2....3....3
..3....0....0....3....4....2....0....3....4....2....1....3....2....4....4....4
..0....1....3....0....1....3....1....1....1....4....0....2....2....3....2....0
..0....2....1....3....2....3....3....2....1....0....2....3....4....0....2....4
..3....2....2....1....3....1....1....0....2....1....4....2....1....0....1....0

Crossrefs

Column 1 is A251421

Sequence in context: A223524 A046207 A030611 * A214011 A344541 A081369

Adjacent sequences: A252174 A252175 A252176 * A252178 A252179 A252180

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 15 2014

Status

approved