A228224 Number of second differences of arrays of length 9 of numbers in 0..n.

511, 19171, 242461, 1688101, 8006491, 29066311, 86929081, 224817481, 519682231, 1098972331, 2162213461, 4007999341, 7067000851, 11941597711, 19452737521, 30694626961, 47097859951, 70501587571, 103235334541, 148211067061

Offset: 1

Author

R. H. Hardin, Aug 16 2013

Keywords

• nonn

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..24

Crossrefs

Row 7 of A228218.

Formula

Empirical: a(n) = 120*n^7 - 42*n^6 - 1158*n^5 + 6945*n^4 - 13980*n^3 + 13512*n^2 - 4887*n + 1.

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

G.f.: x*(511 + 15083*x + 103401*x^2 + 256585*x^3 + 252785*x^4 + 16749*x^5 - 40313*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)