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A034803 Consider the sequence of 4-tuples {0,a,b,c} (c>=a+b; a,b,c>0)) which have the smallest integer 'c' required to reach {k,k,k,k} in n steps under map {r,s,t,u}->{|r-s|,|s-t|,|t-u|,|u-r|}. This sequence gives the second term 'a' of these quadruples. 2
1, 0, 0, 1, 0, 1, 1, 2, 2, 5, 6, 7, 17, 20, 24, 57, 68, 81, 193, 230, 274, 653, 778, 927, 2209, 2632, 3136, 7473, 8904, 10609, 25281, 30122, 35890, 85525, 101902, 121415, 289329, 344732, 410744, 978793, 1166220, 1389537, 3311233, 3945294, 4700770 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,1,0,0,1).

FORMULA

a(n)= Trib(2*q-3)+Trib(2*q-1) if r=0; Trib(2*q-2)+Trib(2*q-1) if r=1; Trib(2*q) if r=2 where q=[(n-1)/3], r=n-1 (mod 3) and Trib is the tribonacci sequence (A000073) with Trib(-3)=0, Trib(-2)=-1, Trib(-1)=1. G.f.: (x^8-2*x^7+3*x^6-x^5+2*x^3-1)/(x^9+x^6+3*x^3-1). Recurrence: a(n)=3*a(n-3)+a(n-6)+a(n-9), n >= 10.

EXAMPLE

a(10)=5 because {0, 5, 14, 31}->{5, 9, 17, 31}->{4, 8, 14, 26}->{4, 6, 12, 22}->{2, 6, 10, 18}->{4, 4, 8, 16}->{0, 4, 8, 12}->{4, 4, 4, 12}->{0, 0, 8, 8}->{0, 8, 0, 8}->{8, 8, 8, 8} ('a'=5 in the first 4-tuple and there is no quadruple with a+b<=c <= 31 and 10 steps).

MATHEMATICA

LinearRecurrence[{0, 0, 3, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 1, 0, 1, 1, 2, 2}, 60] (* Harvey P. Dale, Jun 13 2017 *)

CROSSREFS

A034804, A045794 (or A065678) give the terms 'b' and 'c' respectively.

Sequence in context: A054255 A063177 A249521 * A205885 A239262 A288496

Adjacent sequences:  A034800 A034801 A034802 * A034804 A034805 A034806

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better description, more terms, formula, etc. from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 24 2001

Minor edits from Michael B. Porter, Feb 03 2010

STATUS

approved

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Last modified November 14 14:50 EST 2018. Contains 317208 sequences. (Running on oeis4.)