A226988 Number of n X 2 0..4 arrays of sums of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

10, 42, 120, 313, 729, 1556, 3099, 5818, 10384, 17744, 29198, 46489, 71907, 108408, 159749, 230640, 326914, 455716, 625712, 847319, 1132957, 1497324, 1957695, 2534246, 3250404, 4133224, 5213794, 6527669, 8115335, 10022704, 12301641

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/180)*n^6 + (1/18)*n^5 + (11/36)*n^4 + (877/720)*n^3 + (287/90)*n^2 + (439/84)*n + 4 for n>4.

Conjectures from Colin Barker, Sep 06 2018: (Start)

G.f.: x*(10 - 38*x + 64*x^2 - 31*x^3 - 67*x^4 + 148*x^5 - 137*x^6 + 56*x^7 + 12*x^8 - 26*x^9 + 12*x^10 - 2*x^11) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.

(End)

Example

Some solutions for n=4:
..1..3....0..2....0..2....2..4....1..2....1..2....0..0....0..2....0..0....1..2
..2..3....2..2....1..2....2..2....3..4....2..2....1..2....1..2....1..2....2..2
..2..2....4..2....2..3....3..2....4..4....2..0....2..3....2..3....2..2....2..1
..2..2....4..2....2..4....4..4....4..4....3..2....2..2....2..2....3..2....2..0

Crossrefs

Column 2 of A226992.

Sequence in context: A328536 A163815 A108678 * A358249 A027171 A003822

Adjacent sequences: A226985 A226986 A226987 * A226989 A226990 A226991

Keyword

nonn

Author

R. H. Hardin, Jun 25 2013

Status

approved