OFFSET
1,4
COMMENTS
Another version of A065678, which has further information.
LINKS
Colin Barker, Table of n, a(n) for n = 1..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
Equals [ b(0)+b(2), b(1)+b(2), b(3), b(2)+b(4), b(3)+b(4), b(5), ... ], where b() = A000073. - Peter J. Kernan (pete(AT)theory2.phys.cwru.edu).
From Colin Barker, Feb 18 2015: (Start)
a(n) = 3*a(n-3)+a(n-6)+a(n-9).
G.f.: -x*(x^7-x^6+x^5+x^2+x+1) / (x^9+x^6+3*x^3-1).
(End)
EXAMPLE
a(7) = 9 because {0,1,4,9}->{1,3,5,9}->{2,2,4,8}->{0,2,4,6}->{2,2,2,6}->{0,0,4,4}->{0,4,0,4}->{4,4,4,4} (7 steps and no quadruple with a,b,c,d <= 8 works).
MATHEMATICA
LinearRecurrence[{0, 0, 3, 0, 0, 1, 0, 0, 1}, {1, 1, 1, 3, 3, 4, 9, 11, 13}, 50] (* Harvey P. Dale, May 30 2015 *)
PROG
a=(0 1 0 1); while 1{s=a_3-a_2-a_1; s%2?a*=2:s/=2; a+=s; a_2=a_0+a_1; a_0=0; a_1=s; print a_3}
(PARI) Vec(-x*(x^7-x^6+x^5+x^2+x+1)/(x^9+x^6+3*x^3-1) + O(x^100)) \\ Colin Barker, Feb 18 2015
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Ikuo Kiyokawa (kiyo19(AT)mxr.meshnet.or.jp)
EXTENSIONS
Reference and better description from Erich Friedman
STATUS
approved