login
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.
1
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
1,1
LINKS
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)
EXAMPLE
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
CROSSREFS
Row 3 of A240000.
Sequence in context: A044150 A044531 A304205 * A114241 A127766 A005173
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 30 2014
STATUS
approved