A245951 Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

14, 71, 196, 453, 834, 1435, 2216, 3305, 4630, 6351, 8364, 10861, 13706, 17123, 20944, 25425, 30366, 36055, 42260, 49301, 56914, 65451, 74616, 84793, 95654, 107615, 120316, 134205, 148890, 164851, 181664, 199841, 218926, 239463, 260964, 284005

Offset: 1

Author

R. H. Hardin, Aug 08 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 1 of A245950.

Formula

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

Conjectures from Colin Barker, Nov 05 2018: (Start)

G.f.: x*(14 + 43*x + 40*x^2 + 46*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).

a(n) = 1 + 5*n + 3*n^2 + 6*n^3 for n even.

a(n) = 4 + n + 3*n^2 + 6*n^3 for n odd.

(End)