

A065678


Minimum value t such that all quadruples of Diffy_length >= n have a maximal value >= t.


5



0, 1, 1, 1, 1, 3, 3, 4, 9, 11, 13, 31, 37, 44, 105, 125, 149, 355, 423, 504, 1201, 1431, 1705, 4063, 4841, 5768, 13745, 16377, 19513, 46499, 55403, 66012, 157305, 187427, 223317, 532159, 634061, 755476, 1800281, 2145013, 2555757, 6090307, 7256527
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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]) := [ab, bc, cd, da] (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]).
The "inverse" of sequence A065677 (i.e. A065678(n) = min {m  A065677(m) >= n})


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
A. Behn, C. KribsZaleta and V. Ponomarenko, The convergence of difference boxes, Amer. Math. Monthly 112 (2005), no. 5, 426439.
J. Copeland and J. Haemer, Work: Differences Among Women, SunExpert, 1999, pp. 3843.
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(n3)+a(n6)+a(n9).
G.f.: x*(x1)*(x^8+x^6+x^5+x^4+x^3+3*x^2+2*x+1) / (x^9+x^6+3*x^31).
(End)


EXAMPLE

Since Diffy_length([0,0,0,0]) = 0 and Diffy_length([0,0,0,1]) = 4, we have A065678(1) = A065678(2) = A065678(3) = A065678(4) = 1.


PROG

(PARI) concat(0, Vec(x*(x1)*(x^8+x^6+x^5+x^4+x^3+3*x^2+2*x+1)/(x^9+x^6+3*x^31) + O(x^100))) \\ Colin Barker, Feb 18 2015


CROSSREFS

Cf. A065677.
Sequence in context: A060372 A128036 A045794 * A022598 A107635 A132319
Adjacent sequences: A065675 A065676 A065677 * A065679 A065680 A065681


KEYWORD

nonn,easy


AUTHOR

Jens Voß, Nov 13 2001


STATUS

approved



