A212778 Half the number of 0..4 arrays of length n+2 with second differences nonzero.

56, 252, 1134, 5104, 22972, 103391, 465336, 2094360, 9426184, 42424863, 190943548, 859388488, 3867889651, 17408390437, 78350750657, 352636859298, 1587129076523, 7143265484325, 32150026443551, 144699115914141, 651254025656788

Offset: 1

Author

R. H. Hardin, May 27 2012

Keywords

• nonn

Comments

Column 4 of A212782.

Examples

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

Links

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

Crossrefs

Cf. A212782.

Formula

Empirical: a(n) = 2*a(n-1) + 7*a(n-2) + 14*a(n-3) + 19*a(n-4) + 18*a(n-5) + 5*a(n-6) - 5*a(n-7) - 2*a(n-8).

Empirical g.f.: x*(56 + 140*x + 238*x^2 + 288*x^3 + 234*x^4 + 47*x^5 - 68*x^6 - 25*x^7) / (1 - 2*x - 7*x^2 - 14*x^3 - 19*x^4 - 18*x^5 - 5*x^6 + 5*x^7 + 2*x^8). - Colin Barker, Jul 21 2018