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

1,1

Links

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

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)

Example

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

Crossrefs

Row 7 of A228218.

Sequence in context: A075944 A181128 A228265 * A022525 A069094 A024007

Adjacent sequences: A228221 A228222 A228223 * A228225 A228226 A228227

Keyword

nonn

Author

R. H. Hardin, Aug 16 2013

Status

approved