A240789 - OEIS

A240789

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 zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

3, 4, 5, 10, 13, 14, 30, 32, 36, 67, 79, 97, 173, 191, 232, 402, 464, 580, 960, 1104, 1400, 2250, 2637, 3388, 5280, 6255, 8117, 12342, 14819, 19374, 28826, 35008, 46021, 67233, 82554, 108956, 156715, 194316, 257170, 365065, 456688, 605532, 850096, 1071831

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OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 4*a(n-3) + a(n-5) - 3*a(n-6) - 3*a(n-8) - 4*a(n-9) + a(n-11) + 4*a(n-12) + 3*a(n-14) - 2*a(n-17) for n>19.

Empirical g.f.: x*(3 + 4*x + 5*x^2 - 2*x^3 - 3*x^4 - 9*x^5 - 5*x^6 - 13*x^7 - 6*x^8 - 12*x^9 + 7*x^10 + 12*x^11 + 26*x^12 + 8*x^13 - 8*x^14 - 17*x^15 - 5*x^16 + 5*x^17 + 2*x^18) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x^2 - x^3)*(1 - 2*x^3)*(1 + x^2 - x^3 + x^4 - x^5)). - Colin Barker, Oct 29 2018

EXAMPLE

All solutions for n=4:

..3..3....3..3....3..3....3..3....3..2....3..2....3..3....3..2....3..3....3..3

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

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

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

CROSSREFS

Column 2 of A240792.

Sequence in context: A260823 A359486 A135114 * A191647 A195131 A361666

Adjacent sequences: A240786 A240787 A240788 * A240790 A240791 A240792

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 12 2014

STATUS

approved