A183886 Number of arrangements of n+3 numbers in 0..3 with each number being the sum mod 4 of three others.

16, 292, 2574, 13344, 59518, 250124, 1024174, 4143944, 16671934, 66886900, 267965390, 1072744752, 4292852990, 17175392028, 68710014830, 274857954776, 1099469650494, 4397958390916, 17592001449102, 70368358249024

Offset

1,1

Comments

Column 3 of A183892.

Links

R. H. Hardin, Table of n, a(n) for n = 1..62

Formula

Empirical (for n>=2): 4^(n+3) - (n+3)*2^(n+4) - 2/3*(7*n^3+51*n^2+125*n+108). - Vaclav Kotesovec, Nov 27 2012.

Conjectures from Colin Barker, Apr 05 2018: (Start)

G.f.: 2*x*(8 + 50*x - x^2 - 1488*x^3 + 4469*x^4 - 5336*x^5 + 2996*x^6 - 656*x^7) / ((1 - x)^4*(1 - 2*x)^2*(1 - 4*x)).

a(n) = 12*a(n-1) - 58*a(n-2) + 148*a(n-3) - 217*a(n-4) + 184*a(n-5) - 84*a(n-6) + 16*a(n-7) for n>8.

(End)

Example

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

Crossrefs

Cf. A183892.

Sequence in context: A099279 A202878 A372172 * A230341 A278304 A298192

Adjacent sequences: A183883 A183884 A183885 * A183887 A183888 A183889

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved