A228221 Number of second differences of arrays of length 6 of numbers in 0..n.

63, 665, 3151, 9705, 23351, 47953, 88215, 149681, 238735, 362601, 529343, 747865, 1027911, 1380065, 1815751, 2347233, 2987615, 3750841, 4651695, 5705801, 6929623, 8340465, 9956471, 11796625, 13880751, 16229513, 18864415, 21807801, 25082855

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..177

Formula

Empirical: a(n) = 35*n^4 + 14*n^3 - 17*n^2 + 30*n + 1.

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

G.f.: x*(63 + 350*x + 456*x^2 - 30*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Row 4 of A228218.

Sequence in context: A340902 A381120 A181125 * A022522 A152731 A090028

Adjacent sequences: A228218 A228219 A228220 * A228222 A228223 A228224

Keyword

nonn

Author

R. H. Hardin, Aug 16 2013

Status

approved