A250320 T(n,k)=Number of length n+2 0..k arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

2, 5, 8, 8, 25, 8, 13, 60, 41, 24, 18, 117, 104, 161, 42, 25, 200, 233, 652, 487, 104, 32, 321, 436, 1773, 2432, 1689, 212, 41, 480, 745, 3916, 8767, 12820, 5849, 464, 50, 681, 1152, 7969, 24126, 57833, 61092, 19981, 950, 61, 940, 1733, 14452, 57305, 197848

Offset: 1

Author

R. H. Hardin, Nov 18 2014

Keywords

• nonn
• tabl

Comments

Table starts

....2......5.......8.......13........18.........25.........32........41

....8.....25......60......117.......200........321........480.......681

....8.....41.....104......233.......436........745.......1152......1733

...24....161.....652.....1773......3916.......7969......14452.....24293

...42....487....2432.....8767.....24126......57305.....119004....228401

..104...1689...12820....57833....197848.....558541....1357424...2953265

..212...5849...61092...363457...1559080....5237161...14866258..37065983

..464..19981..300616..2317841..12424332...50020061..166783380.476368553

..950..67459.1423966.14305925..95711098..461868677.1809575752

.1968.221953.6523576.85334033.709795516.4110975765

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Row 1 is A000982(n+1)

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -6*a(n-3) +3*a(n-4) +3*a(n-5) -2*a(n-6)

Empirical for row n:

n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2

n=2: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8); also a cubic polynomial plus a linear quasipolynomial with period 3