A228261 Number of third differences of arrays of length 5 of numbers in 0..n.

31, 143, 319, 565, 881, 1267, 1723, 2249, 2845, 3511, 4247, 5053, 5929, 6875, 7891, 8977, 10133, 11359, 12655, 14021, 15457, 16963, 18539, 20185, 21901, 23687, 25543, 27469, 29465, 31531, 33667, 35873, 38149, 40495, 42911, 45397, 47953, 50579, 53275

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 35*n^2 + n + 1 for n>1.

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

G.f.: x*(31 + 50*x - 17*x^2 + 6*x^3) / (1 - x)^3.

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

(End)

Example

Some solutions for n=4:
..0...-6...-2...-9...-4...-3...-7...-3....9....8...-1....5...-3....8..-13...-2
.-2...-2....8....7...-4...-9...13....2....2..-10....8....3...-5...-6....3....0

Crossrefs

Row 2 of A228260.

Sequence in context: A182916 A233303 A185521 * A185513 A234122 A142758

Adjacent sequences: A228258 A228259 A228260 * A228262 A228263 A228264

Keyword

nonn

Author

R. H. Hardin, Aug 19 2013

Status

approved