A227060 T(n,k)=Number of nXk -2..2 arrays of 2X2 subblock diagonal sums minus antidiagonal sums for some (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order

4, 10, 10, 20, 40, 20, 35, 124, 124, 35, 56, 329, 643, 329, 56, 84, 777, 2934, 2934, 777, 84, 120, 1673, 11810, 24511, 11810, 1673, 120, 165, 3341, 42295, 183000, 183000, 42295, 3341, 165, 220, 6269, 136553, 1202223, 2625106, 1202223, 136553, 6269, 220

Offset

1,1

Comments

Table starts

...4....10......20........35..........56............84..............120

..10....40.....124.......329.........777..........1673.............3341

..20...124.....643......2934.......11810.........42295...........136553

..35...329....2934.....24511......183000.......1202223..........6979049

..56...777...11810....183000.....2625106......33345171........371484306

..84..1673...42295...1202223....33345171.....836488605......18470742252

.120..3341..136553...6979049...371484306...18470742252.....818230288186

.165..6269..402898..36211854..3651371505..358194085953...31887670171357

.220.11164.1099681.170079551.32017940207.6148026957082.1096628939510030

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = (1/6)*n^3 + 1*n^2 + (11/6)*n + 1

k=2: [polynomial of degree 7]

k=3: [polynomial of degree 15]

Example

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

Crossrefs

Column 1 is A000292(n+1)

Sequence in context: A310335 A352753 A310336 * A278727 A184129 A202581

Adjacent sequences: A227057 A227058 A227059 * A227061 A227062 A227063

Keyword

nonn,tabl

Author

R. H. Hardin Jun 30 2013

Status

approved