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A045794 Consider all quadruples {a,b,c,d} which reach {k,k,k,k} in n steps under map {a,b,c,d}->{|a-b|,|b-c|,|c-d|,|d-a|}; look at max{a,b,c,d}; sequence gives minimal value of this. 5
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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A185395 A060372 A128036 * A065678 A022598 A107635

Adjacent sequences:  A045791 A045792 A045793 * A045795 A045796 A045797

KEYWORD

nonn,nice,easy

AUTHOR

Ikuo Kiyokawa (kiyo19(AT)mxr.meshnet.or.jp)

EXTENSIONS

Reference and better description from Erich Friedman

STATUS

approved

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)