A240395 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 two plus the sum of the elements diagonally to its northwest, modulo 4.

2, 12, 32, 62, 118, 206, 351, 568, 882, 1322, 1921, 2716, 3748, 5062, 6707, 8736, 11206, 14178, 17717, 21892, 26776, 32446, 38983, 46472, 55002, 64666, 75561, 87788, 101452, 116662, 133531, 152176, 172718, 195282, 219997, 246996, 276416, 308398

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/6)*n^4 - (5/6)*n^3 + (13/3)*n^2 + (31/3)*n - 48 for n>5.

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

G.f.: x*(2 + 2*x - 8*x^2 + 2*x^3 + 18*x^4 - 26*x^5 + 29*x^6 - 29*x^7 + 20*x^8 - 6*x^9) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>10.

(End)

Example

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

Crossrefs

Row 3 of A240394.

Sequence in context: A254962 A139323 A225525 * A009331 A154252 A013198

Adjacent sequences: A240392 A240393 A240394 * A240396 A240397 A240398

Keyword

nonn

Author

R. H. Hardin, Apr 04 2014

Status

approved