A228214 Number of second differences of arrays of length n + 2 of numbers in 0..4.

17, 177, 1429, 9705, 58141, 320481, 1688101, 8717049, 44633821, 227363409, 1153594261, 5835080169, 29443836301, 148292923329, 745759583941, 3745977788889, 18798608421181, 94267920012849, 472439111692021

Offset: 1

Author

R. H. Hardin, Aug 16 2013

Keywords

• nonn

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..137

Crossrefs

Column 4 of A228218.

Formula

Empirical: a(n) = 9*a(n-1) - 20*a(n-2) = A005060(n+2) for n>9.

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

G.f.: x*(17 + 24*x + 176*x^2 + 384*x^3 - 624*x^4 - 8688*x^5 - 33408*x^6 - 66240*x^7 - 57600*x^8) / ((1 - 4*x)*(1 - 5*x)).

a(n) = 5^(2+n) - 4^(2+n) for n>7.

(End)