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

1,1

Links

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

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)

Example

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

Crossrefs

Row 5 of A228218.

Sequence in context: A258015 A181126 A228263 * A022523 A090029 A152726

Adjacent sequences: A228219 A228220 A228221 * A228223 A228224 A228225

Keyword

nonn

Author

R. H. Hardin, Aug 16 2013

Status

approved