A245871 Number of length 2+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

10, 45, 100, 193, 318, 493, 712, 993, 1330, 1741, 2220, 2785, 3430, 4173, 5008, 5953, 7002, 8173, 9460, 10881, 12430, 14125, 15960, 17953, 20098, 22413, 24892, 27553, 30390, 33421, 36640, 40065, 43690, 47533, 51588, 55873, 60382, 65133, 70120, 75361

Offset: 1

Author

R. H. Hardin, Aug 04 2014

Keywords

• nonn

Examples

			Some solutions for n=10:
..9....1....8....0....9....0...10....4....3....5....8....4....3...10....3....9
..0....9....4....6....0...10....0....4....4....5....2....4....4....2....1....5
.10....1....6....4...10....0...10....6....6....9...10....6....6....8....9....1
.10....0....0....0....1....3....4....3....0....1....8....1....6....8....7....5
		

Links

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

Crossrefs

Row 2 of A245869.

Formula

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

Conjectures from Colin Barker, Nov 04 2018: (Start)

G.f.: x*(10 + 15*x - 15*x^2 + 3*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = 1 + 4*n + 7*n^2 + n^3 for n even.

a(n) = -2 + 4*n + 7*n^2 + n^3 for n odd.

(End)