A239844 - OEIS

A239844

Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4.

3, 8, 17, 35, 64, 109, 176, 272, 405, 584, 819, 1121, 1502, 1975, 2554, 3254, 4091, 5082, 6245, 7599, 9164, 10961, 13012, 15340, 17969, 20924, 24231, 27917, 32010, 36539, 41534, 47026, 53047, 59630, 66809, 74619, 83096, 92277, 102200, 112904, 124429

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OFFSET

1,1

LINKS

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

W. Kuszmaul, Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations, arXiv preprint arXiv:1509.08216, 2015

FORMULA

Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (53/12)*n - 6 for n>2.

Conjectures from Colin Barker, Oct 26 2018: (Start)

G.f.: x*(1 - x + x^2)*(3 - 4*x + 4*x^3 - 2*x^4) / (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>7.

(End)

EXAMPLE

Some solutions for n=4:

..0..0....3..3....0..3....0..0....0..3....0..0....0..0....0..0....0..0....0..3

..0..0....3..2....3..3....0..0....0..3....0..0....0..3....3..3....0..0....3..3

..0..3....0..0....3..2....0..0....3..1....0..3....3..3....3..3....0..3....3..2

..3..1....0..3....0..3....0..0....3..3....3..3....3..2....0..2....0..3....0..0

CROSSREFS

Column 2 of A239849.

Sequence in context: A145071 A182734 A327608 * A182616 A159217 A052996

Adjacent sequences: A239841 A239842 A239843 * A239845 A239846 A239847

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 28 2014

STATUS

approved