login
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
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 15 2014
STATUS
approved