A228222 Number of second differences of arrays of length 7 of numbers in 0..n.

127, 2059, 14053, 58141, 176851, 439927, 951049, 1854553, 3342151, 5659651, 9113677, 14078389, 21002203, 30414511, 42932401, 59267377, 80232079, 106747003, 139847221, 180689101, 230557027, 290870119, 363188953, 449222281, 550833751

Offset: 1

Author

R. H. Hardin, Aug 16 2013

Keywords

• nonn

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..63

Crossrefs

Row 5 of A228218.

Formula

Empirical: a(n) = 56*n^5 + 14*n^4 - 108*n^3 + 289*n^2 - 125*n + 1.

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

G.f.: x*(127 + 1297*x + 3604*x^2 + 2168*x^3 - 475*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)