A245953 Number of length 3+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

48, 545, 2304, 7769, 18384, 39721, 73728, 130193, 211440, 332561, 496128, 723625, 1017744, 1407449, 1895424, 2519201, 3281328, 4228993, 5364480, 6745721, 8374608, 10320905, 12585984, 15252529, 18321264, 21888881, 25955328, 30632393, 35919120

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 05 2018: (Start)

G.f.: x*(48 + 401*x + 669*x^2 + 1241*x^3 - 851*x^4 - 557*x^5 + 7*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3).

a(n) = 1 + 26*n - 17*n^2 + 24*n^3 + 21*n^4 + n^5 for n even.

a(n) = 39 - n - 36*n^2 + 24*n^3 + 21*n^4 + n^5 for n odd.

(End)

Example

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

Crossrefs

Row 3 of A245950.

Sequence in context: A189346 A334713 A266210 * A192832 A352847 A042949

Adjacent sequences: A245950 A245951 A245952 * A245954 A245955 A245956

Keyword

nonn

Author

R. H. Hardin, Aug 08 2014

Status

approved