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

1,1

Links

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

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)

Example

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

Crossrefs

Row 1 of A245950.

Sequence in context: A222989 A245950 A041372 * A352869 A212572 A186707

Adjacent sequences: A245948 A245949 A245950 * A245952 A245953 A245954

Keyword

nonn

Author

R. H. Hardin, Aug 08 2014

Status

approved