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A221592
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Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less.
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1
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0, 13, 35, 169, 651, 2715, 11011, 45099, 184063, 752155, 3072247, 12550859, 51270383, 209444163, 855592375, 3495156539, 14277953839, 58326437619, 238267540647, 973339457803, 3976159254687, 16242886662499, 66353319815959, 271057918757755, 1107290419059023
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).
G.f.: x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - Colin Barker, Jan 31 2017
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EXAMPLE
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Some solutions for n=6
..3....3....2....1....4....4....3....3....3....3....4....4....2....2....3....3
..2....3....1....0....3....3....4....2....4....4....3....3....2....3....2....2
..1....0....4....2....4....2....0....3....4....2....4....2....2....4....3....3
..1....1....4....3....2....1....0....1....3....3....0....0....4....4....0....3
..3....2....2....0....3....0....1....1....3....0....0....0....3....4....1....4
..3....1....3....1....2....0....0....0....3....1....0....1....2....4....1....4
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PROG
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(PARI) concat(0, Vec(x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6) + O(x^30))) \\ Colin Barker, Jan 31 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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