A227103 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of two, with rows and columns of the latter in lexicographically nondecreasing order

2, 4, 4, 7, 15, 7, 11, 48, 48, 11, 16, 136, 239, 136, 16, 22, 341, 1084, 1084, 341, 22, 29, 771, 4444, 8427, 4444, 771, 29, 37, 1606, 16366, 60039, 60039, 16366, 1606, 37, 46, 3133, 54500, 384591, 754758, 384591, 54500, 3133, 46, 56, 5789, 166271, 2209056

Offset

1,1

Comments

Table starts

..2....4......7.......11........16.........22.........29..........37.........46

..4...15.....48......136.......341........771.......1606........3133.......5789

..7...48....239.....1084......4444......16366......54500......166271.....470106

.11..136...1084.....8427.....60039.....384591....2209056....11456481...54141062

.16..341...4444....60039....754758....8638999...89104481...828893716.6983821643

.22..771..16366...384591...8638999..180409504.3428152304.58981679762

.29.1606..54500..2209056..89104481.3428152304

.37.3133.166271.11456481.828893716

.46.5789.470106.54141062

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

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

k=2: [polynomial of degree 7] for n>3

k=3: [polynomial of degree 15] for n>5

k=4: [polynomial of degree 31] for n>13

Example

Some solutions for n=4 k=4
..0..0..0..0....0..1..0..0....0..1..0..0....0..0..0..1....0..0..0..1
..0..1..0..0....0..1..0..0....1..0..1..0....0..1..1..0....0..0..1..0
..1..0..1..0....0..0..0..0....1..1..1..0....1..1..1..0....0..0..0..0
..1..0..0..1....0..0..0..1....0..1..1..0....0..1..0..0....0..0..1..1

Crossrefs

Column 1 is A000124

Sequence in context: A205744 A237859 A240338 * A223644 A223637 A223620

Adjacent sequences: A227100 A227101 A227102 * A227104 A227105 A227106

Keyword

nonn,tabl

Author

R. H. Hardin Jul 01 2013

Status

approved