A228223 Number of second differences of arrays of length 8 of numbers in 0..n.

255, 6305, 58975, 320481, 1225631, 3693505, 9399615, 21108545, 43067071, 81457761, 144913055, 245089825, 397304415, 621228161, 941643391, 1389259905, 2001591935, 2823895585, 3910166751, 5324199521, 7140705055, 9446490945

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..34

Formula

Empirical: a(n) = 84*n^6 - 402*n^4 + 1656*n^3 - 1860*n^2 + 776*n + 1.

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

G.f.: x*(255 + 4520*x + 20195*x^2 + 31136*x^3 + 8989*x^4 - 4616*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 6 of A228218.

Sequence in context: A075941 A181127 A228264 * A022524 A261032 A069093

Adjacent sequences: A228220 A228221 A228222 * A228224 A228225 A228226

Keyword

nonn

Author

R. H. Hardin, Aug 16 2013

Status

approved