A246480 Number of length 1+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

2, 10, 60, 172, 462, 966, 1880, 3256, 5370, 8290, 12372, 17700, 24710, 33502, 44592, 58096, 74610, 94266, 117740, 145180, 177342, 214390, 257160, 305832, 361322, 423826, 494340, 573076, 661110, 758670, 866912, 986080, 1117410, 1261162

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7).

Conjectures from Colin Barker, Nov 06 2018: (Start)

G.f.: 2*x*(1 + 2*x + 16*x^2 + 6*x^3 + 23*x^4) / ((1 - x)^5*(1 + x)^2).

a(n) = -n + 3*n^2 - 2*n^3 + n^4 for n even.

a(n) = -3 + 3*n + 3*n^2 - 2*n^3 + n^4 for n odd.

(End)

Example

Some solutions for n=6:
..6....4....6....1....4....4....1....5....4....0....2....1....1....4....0....5
..3....1....5....4....5....0....0....3....4....4....2....2....3....4....4....5
..5....4....5....0....0....5....3....5....3....3....1....3....2....6....5....5
..2....4....2....4....5....5....4....5....5....5....0....2....0....4....5....5

Crossrefs

Row 1 of A246479.

Sequence in context: A240605 A095993 A029725 * A303361 A026161 A025188

Adjacent sequences: A246477 A246478 A246479 * A246481 A246482 A246483

Keyword

nonn

Author

R. H. Hardin, Aug 27 2014

Status

approved