A245876 Number of length 7+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

110, 2967, 12100, 40901, 97602, 214315, 404264, 727017, 1200310, 1920671, 2909100, 4309357, 6143690, 8614131, 11741392, 15797585, 20798334, 27098407, 34704020, 44065941, 55175890, 68594747, 84293880, 102959161, 124534982, 149847855

Offset: 1

Author

R. H. Hardin, Aug 04 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 7 of A245869.

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*(110 + 2747*x + 5836*x^2 + 8680*x^3 + 3456*x^4 - 2178*x^5 - 1148*x^6 - 224*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).

a(n) = 1 + 37*n + 43*n^2 + 126*n^3 + 89*n^4 + 9*n^5 for n even.

a(n) = 7 - 76*n - 41*n^2 + 122*n^3 + 89*n^4 + 9*n^5 for n odd.

(End)