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A196597 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,2,4,0,3 for x=0,1,2,3,4. 2
1, 7, 37, 129, 667, 2783, 12515, 55513, 245289, 1088893, 4822927, 21375111, 94733197, 419809045, 1860501635, 8245134291, 36539888027, 161933744951, 717640229759, 3180361894219, 14094387608445, 62461999300427 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Every 0 is next to 0 1's, every 1 is next to 1 2's, every 2 is next to 2 4's, every 3 is next to 3 0's, every 4 is next to 4 3's.
Column 4 of A196601.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 9*a(n-2) + 10*a(n-3) - 9*a(n-4) - 3*a(n-5) + 6*a(n-6) - 5*a(n-7) + a(n-8).
Empirical g.f.: x*(1 + 5*x + 14*x^2 - 18*x^3 + 15*x^4 - 16*x^5 + 4*x^6 + x^7) / (1 - 2*x - 9*x^2 - 10*x^3 + 9*x^4 + 3*x^5 - 6*x^6 + 5*x^7 - x^8). - Colin Barker, Mar 01 2018
EXAMPLE
Some solutions for n=5:
..0..3..0..0....0..3..0..0....0..3..0..0....0..3..0..0....0..0..3..0
..3..0..0..3....0..0..0..0....3..0..0..0....0..0..0..0....3..0..0..0
..0..3..3..0....0..0..0..0....0..3..3..0....0..3..3..0....0..0..0..0
..0..0..0..3....0..0..0..3....3..0..0..0....0..0..0..0....0..0..0..3
..0..0..3..0....0..0..0..0....0..3..0..0....0..0..3..0....0..0..0..0
CROSSREFS
Cf. A196601.
Sequence in context: A136204 A139891 A082113 * A143991 A243893 A012885
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 04 2011
STATUS
approved

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Last modified April 22 02:54 EDT 2024. Contains 371887 sequences. (Running on oeis4.)