A228221 Number of second differences of arrays of length 6 of numbers in 0..n.

63, 665, 3151, 9705, 23351, 47953, 88215, 149681, 238735, 362601, 529343, 747865, 1027911, 1380065, 1815751, 2347233, 2987615, 3750841, 4651695, 5705801, 6929623, 8340465, 9956471, 11796625, 13880751, 16229513, 18864415, 21807801, 25082855

Offset: 1

Author

R. H. Hardin, Aug 16 2013

Keywords

• nonn

Examples

			Some solutions for n=4:
..4....5....6...-2...-5....5...-6....5....7...-2....0....3...-1....4...-2....3
..0...-2...-3...-3...-1....0....3...-3...-5....3...-4...-5....5....0....1...-2
.-4....5....0....1....2...-4....2....3....5...-1....4....0...-6...-3....1...-2
..1...-8....5....1...-1....2...-5...-4...-7...-2....2....3....7....0....4....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..177

Crossrefs

Row 4 of A228218.

Formula

Empirical: a(n) = 35*n^4 + 14*n^3 - 17*n^2 + 30*n + 1.

Conjectures from Colin Barker, Sep 10 2018: (Start)

G.f.: x*(63 + 350*x + 456*x^2 - 30*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)