A200273 Number of 0..n arrays x(0..5) of 6 elements with zero 3rd differences.

2, 3, 6, 9, 14, 25, 36, 47, 64, 87, 110, 143, 176, 209, 258, 311, 364, 431, 498, 575, 666, 761, 856, 969, 1092, 1219, 1364, 1513, 1662, 1847, 2032, 2221, 2432, 2647, 2876, 3135, 3394, 3657, 3946, 4257, 4568, 4913, 5258, 5607, 6004, 6409, 6814, 7257, 7700, 8169

Offset: 1

Author

R. H. Hardin, Nov 15 2011

Keywords

• nonn

Comments

Row 4 of A200272.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A200272.

Formula

Empirical: a(n) = a(n-3) +a(n-5) +a(n-6) -a(n-8) -a(n-9) +a(n-10) -a(n-11) -a(n-13) +a(n-14) -a(n-15) -a(n-16) +a(n-18) +a(n-19) +a(n-21) -a(n-24).

Empirical g.f.: x*(2 + 3*x + 6*x^2 + 7*x^3 + 11*x^4 + 17*x^5 + 22*x^6 + 24*x^7 + 26*x^8 + 33*x^9 + 31*x^10 + 32*x^11 + 26*x^12 + 26*x^13 + 21*x^14 + 15*x^15 + 10*x^16 + 8*x^17 + 6*x^18 + 3*x^19 + 3*x^20 + x^21 - x^23) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, May 20 2018