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A240359
Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4.
1
4, 15, 43, 111, 261, 571, 1171, 2278, 4235, 7570, 13076, 21918, 35774, 57018, 88954, 136111, 204610, 302615, 440881, 633413, 898251, 1258397, 1742901, 2388124, 3239197, 4351696, 5793554, 7647232, 10012172, 13007556, 16775396, 21483981
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/40320)*n^8 - (1/2016)*n^7 + (7/576)*n^6 - (23/360)*n^5 + (1327/5760)*n^4 + (1271/288)*n^3 - (25027/672)*n^2 + (127387/840)*n - 223 for n>4.
Conjectures from Colin Barker, Oct 27 2018: (Start)
G.f.: x*(4 - 21*x + 52*x^2 - 72*x^3 + 54*x^4 - 8*x^5 - 32*x^6 + 55*x^7 - 67*x^8 + 66*x^9 - 46*x^10 + 20*x^11 - 4*x^12) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>13.
(End)
EXAMPLE
Some solutions for n=4:
..0..0....0..3....3..1....0..3....3..3....3..1....3..1....0..0....3..1....0..0
..0..3....0..3....0..2....0..3....0..0....0..2....0..2....0..3....0..2....0..0
..3..3....3..1....3..3....3..1....3..3....0..3....0..3....3..3....0..0....0..3
..0..2....0..2....3..2....3..2....3..2....3..3....0..3....0..3....0..3....0..0
CROSSREFS
Column 2 of A240364.
Sequence in context: A187928 A213498 A294259 * A282522 A329523 A331317
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 04 2014
STATUS
approved