A240002 Number of 3 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

12, 61, 190, 526, 1262, 2766, 5647, 10878, 19971, 35180, 59780, 98414, 157524, 245879, 375214, 560995, 823326, 1188015, 1687817, 2363873, 3267365, 4461408, 6023201, 8046460, 10644157, 13951590, 18129810, 23369432, 29894858, 37968941

Offset: 1

Author

R. H. Hardin, Mar 30 2014

Keywords

• nonn

Examples

			Some solutions for n=5:
..0..3..3..0..0....0..3..3..0..0....0..0..0..0..3....0..3..3..0..0
..0..3..3..1..3....0..0..3..1..3....0..3..3..0..0....0..3..2..3..3
..0..3..3..2..0....0..0..2..1..2....0..0..2..1..3....0..3..1..0..2
		

Links

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

Crossrefs

Row 3 of A240000.

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/2016)*n^7 + (7/576)*n^6 + (17/360)*n^5 + (6367/5760)*n^4 - (935/288)*n^3 + (28145/672)*n^2 - (114913/840)*n + 237 for n>6.

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

G.f.: x*(12 - 47*x + 73*x^2 + 4*x^3 - 244*x^4 + 558*x^5 - 737*x^6 + 651*x^7 - 375*x^8 + 86*x^9 + 91*x^10 - 128*x^11 + 80*x^12 - 27*x^13 + 4*x^14) / (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>15.

(End)