A240193 Number of 3 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

3, 12, 37, 129, 478, 1908, 7868, 32888, 138292, 583040, 2461028, 10393720, 43907108, 185502448, 783769556, 3311604104, 13992449972, 59122342816, 249810507844, 1055529401752, 4459952527044, 18844744947024, 79625166220340

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 27*a(n-2) + 29*a(n-3) + 6*a(n-4) - 32*a(n-5) + 16*a(n-6) for n>9.

Empirical g.f.: x*(3 - 15*x + 10*x^2 + 33*x^3 - 50*x^4 + 40*x^5 - 25*x^6 - 52*x^7 + 72*x^8) / ((1 - x)*(1 - 2*x)*(1 - 6*x + 7*x^2 + 4*x^3 - 8*x^4)). - Colin Barker, Oct 27 2018

Example

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

Crossrefs

Row 3 of A240192.

Sequence in context: A022727 A290930 A264423 * A319077 A368097 A008907

Adjacent sequences: A240190 A240191 A240192 * A240194 A240195 A240196

Keyword

nonn

Author

R. H. Hardin, Apr 02 2014

Status

approved