A246738 Number of length 1+4 0..n arrays with no pair in any consecutive five terms totalling exactly n.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences: A246735 A246736 A246737 * A246739 A246740 A246741

Keyword

nonn

Author

R. H. Hardin, Sep 02 2014

Status

approved