A240333 Number of n X 2 0..3 arrays with no element equal to two plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

4, 15, 48, 125, 284, 582, 1097, 1932, 3219, 5123, 7846, 11631, 16766, 23588, 32487, 43910, 58365, 76425, 98732, 126001, 159024, 198674, 245909, 301776, 367415, 444063, 533058, 635843, 753970, 889104, 1043027, 1217642, 1414977, 1637189

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/30)*n^5 + (1/24)*n^4 + (23/12)*n^3 - (193/24)*n^2 + (581/20)*n - 30 for n>2.

Conjectures from Colin Barker, Oct 27 2018: (Start)

G.f.: x*(4 - 9*x + 18*x^2 - 18*x^3 + 14*x^4 - 6*x^5 - x^6 + 2*x^7) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.

(End)

Example

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

Crossrefs

Column 2 of A240338.

Sequence in context: A307075 A219903 A238807 * A227099 A225976 A093967

Adjacent sequences: A240330 A240331 A240332 * A240334 A240335 A240336

Keyword

nonn

Author

R. H. Hardin, Apr 04 2014

Status

approved