OFFSET
0,6
COMMENTS
Another version of A045794, which has further information including a formula.
For quadruples of nonnegative integers a, b, c, d we let diffy([a, b, c, d]) := [|a-b|, |b-c|, |c-d|, |d-a|] (i.e. the quadruple of absolute differences of neighboring values, cyclically speaking) and Diffy_length([a, b, c, d]) := min { n in N | diffy^n([a, b, c, d]) = [0, 0, 0, 0] } (i.e. the minimum number of diffy iterations needed to convert [a, b, c, d] into [0, 0, 0, 0]).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
A. Behn, C. Kribs-Zaleta and V. Ponomarenko, The convergence of difference boxes, Amer. Math. Monthly 112 (2005), no. 5, 426-439.
J. Copeland and J. Haemer, Work: Differences Among Women, SunExpert, 1999, pp. 38-43.
Raymond Greenwell, The Game of Diffy, Math. Gazette, Oct 1989, p. 222.
Peter J. Kernan (pete(AT)theory2.phys.cwru.edu), Algorithm and code [Broken link]
Dawn J. Lawrie, The Diffy game.
Univ. Mass. Computer Science 121, The Diffy Game [Broken link]
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,1,0,0,1).
FORMULA
From Colin Barker, Feb 18 2015: (Start)
a(n) = 3*a(n-3)+a(n-6)+a(n-9).
G.f.: x*(x-1)*(x^8+x^6+x^5+x^4+x^3+3*x^2+2*x+1) / (x^9+x^6+3*x^3-1).
(End)
EXAMPLE
PROG
(PARI) concat(0, Vec(x*(x-1)*(x^8+x^6+x^5+x^4+x^3+3*x^2+2*x+1)/(x^9+x^6+3*x^3-1) + O(x^100))) \\ Colin Barker, Feb 18 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jens Voß, Nov 13 2001
STATUS
approved