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

1,1

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 + (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

Adjacent sequences: A239999 A240000 A240001 * A240003 A240004 A240005

Keyword

nonn

Author

R. H. Hardin, Mar 30 2014

Status

approved