A245954 Number of length 4+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

88, 1501, 7744, 31465, 82968, 199141, 397504, 754321, 1292440, 2144941, 3335808, 5074681, 7380184, 10560565, 14620288, 19990561, 26650584, 35181181, 45522880, 58435081, 73803928, 92598661, 114633024, 141119665, 171779608, 208104781

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).

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

G.f.: x*(88 + 1325*x + 4478*x^2 + 12178*x^3 + 8990*x^4 + 2708*x^5 - 310*x^6 - 658*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).

a(n) = 1 + 34*n + 6*n^2 - 16*n^3 + 66*n^4 + 15*n^5 for n even.

a(n) = 58 + 57*n - 80*n^2 - 28*n^3 + 66*n^4 + 15*n^5 for n odd.

(End)

Example

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

Crossrefs

Row 4 of A245950

Sequence in context: A239274 A235018 A228810 * A248047 A107422 A210006

Adjacent sequences: A245951 A245952 A245953 * A245955 A245956 A245957

Keyword

nonn

Author

R. H. Hardin, Aug 08 2014

Status

approved