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A297434
Number of 4 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.
1
1, 4, 22, 42, 105, 349, 1057, 2834, 8216, 24556, 71651, 207409, 608985, 1791636, 5251548, 15401954, 45271039, 133066199, 390990659, 1149260888, 3379206474, 9935995300, 29215600841, 85913309363, 252656693545, 743030170284
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-4) - 33*a(n-5) - 7*a(n-6) + 21*a(n-7) + 3*a(n-8) + 2*a(n-9) + 3*a(n-10) + 5*a(n-11) - 2*a(n-12).
Empirical g.f.: x*(1 + x + 9*x^2 - 28*x^3 - 44*x^4 + 21*x^5 + 22*x^6 + 5*x^7 + 5*x^8 + 8*x^9 + 3*x^10 - 2*x^11) / ((1 + x)*(1 - 4*x + 3*x^2 - 3*x^3 + 2*x^4 + 31*x^5 - 24*x^6 + 3*x^7 - 6*x^8 + 4*x^9 - 7*x^10 + 2*x^11)). - Colin Barker, Feb 28 2019
EXAMPLE
Some solutions for n=5:
..0..0..0..0..0. .0..0..0..0..0. .0..1..1..0..0. .0..0..0..0..0
..0..0..0..0..0. .0..1..1..1..0. .0..1..1..0..0. .0..0..0..0..0
..1..1..1..0..0. .0..0..1..0..0. .0..0..0..0..0. .1..1..0..0..0
..0..1..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..1..1..0..0
CROSSREFS
Row 4 of A297431.
Sequence in context: A350521 A163484 A326737 * A020173 A290709 A163433
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 30 2017
STATUS
approved