A212783 Half the number of 0..n arrays of length 4 with second differences nonzero.

5, 27, 99, 252, 546, 1034, 1803, 2925, 4517, 6670, 9528, 13204, 17869, 23655, 30763, 39344, 49626, 61782, 76067, 92673, 111885, 133914, 159072, 187592, 219813, 255987, 296483, 341572, 391650, 447010, 508075, 575157, 648709, 729062, 816696, 911964

Offset: 1

Author

R. H. Hardin, May 27 2012

Keywords

• nonn

Comments

Row 2 of A212782.

Examples

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

Links

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

Crossrefs

Cf. A212782.

Formula

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

Empirical g.f.: x*(5 + 17*x + 40*x^2 + 42*x^3 + 29*x^4 + 9*x^5 + 2*x^6) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jul 21 2018