A240359 Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4.

4, 15, 43, 111, 261, 571, 1171, 2278, 4235, 7570, 13076, 21918, 35774, 57018, 88954, 136111, 204610, 302615, 440881, 633413, 898251, 1258397, 1742901, 2388124, 3239197, 4351696, 5793554, 7647232, 10012172, 13007556, 16775396, 21483981

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (7/576)*n^6 - (23/360)*n^5 + (1327/5760)*n^4 + (1271/288)*n^3 - (25027/672)*n^2 + (127387/840)*n - 223 for n>4.

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

G.f.: x*(4 - 21*x + 52*x^2 - 72*x^3 + 54*x^4 - 8*x^5 - 32*x^6 + 55*x^7 - 67*x^8 + 66*x^9 - 46*x^10 + 20*x^11 - 4*x^12) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>13.

(End)

Example

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

Crossrefs

Column 2 of A240364.

Sequence in context: A187928 A213498 A294259 * A282522 A329523 A331317

Adjacent sequences: A240356 A240357 A240358 * A240360 A240361 A240362

Keyword

nonn

Author

R. H. Hardin, Apr 04 2014

Status

approved