A240001 - OEIS

A240001

Number of 2 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.

5, 13, 25, 42, 65, 95, 133, 180, 237, 305, 385, 478, 585, 707, 845, 1000, 1173, 1365, 1577, 1810, 2065, 2343, 2645, 2972, 3325, 3705, 4113, 4550, 5017, 5515, 6045, 6608, 7205, 7837, 8505, 9210, 9953, 10735, 11557, 12420, 13325, 14273, 15265, 16302

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OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n.

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

G.f.: x*(5 - 7*x + 3*x^2) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

EXAMPLE

Some solutions for n=5:

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

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

CROSSREFS

Row 2 of A240000.

Sequence in context: A146875 A241233 A064276 * A301685 A102724 A147031

Adjacent sequences: A239998 A239999 A240000 * A240002 A240003 A240004

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 30 2014

STATUS

approved