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

Author

R. H. Hardin, Aug 08 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 4 of A245950

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)