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

1,1

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

Links

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

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

Example

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

Crossrefs

Row 1 is A000982(n+1)

Sequence in context: A351391 A046825 A374442 * A250561 A131716 A011279

Adjacent sequences: A250317 A250318 A250319 * A250321 A250322 A250323

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 18 2014

Status

approved