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A246738
Number of length 1+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.
1
2, 12, 124, 424, 1566, 3876, 9368, 18768, 36250, 63100, 106452, 168312, 259574, 383124, 554416, 777376, 1072818, 1445868, 1923500, 2512200, 3245902, 4132612, 5214024, 6499824, 8040266, 9846876, 11979268, 14450968, 17331750, 20637300
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).
Conjectures from Colin Barker, Nov 06 2018: (Start)
G.f.: 2*x*(1 + 3*x + 44*x^2 + 34*x^3 + 189*x^4 + 43*x^5 + 166*x^6) / ((1 - x)^6*(1 + x)^3).
a(n) = 10*n - 20*n^2 + 15*n^3 - 5*n^4 + n^5 for n even.
a(n) = 16 - 15*n - 10*n^2 + 15*n^3 - 5*n^4 + n^5 for n odd.
(End)
EXAMPLE
Some solutions for n=4:
..1....1....2....2....2....0....4....4....3....3....3....0....3....4....1....2
..0....0....0....3....1....3....1....4....3....4....3....3....3....3....4....3
..2....2....1....3....0....0....2....2....4....2....2....3....0....3....4....4
..0....1....0....0....0....3....1....1....4....4....3....0....0....3....2....3
..1....0....0....3....0....0....1....1....3....3....4....3....3....4....1....4
CROSSREFS
Row 1 of A246737.
Sequence in context: A375897 A013469 A372178 * A039933 A364397 A214223
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 02 2014
STATUS
approved