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Search: id:A034803
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| A034803 |
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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|}. Thhis sequence gives the second term 'a' of these quadruples. |
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2
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| 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
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OFFSET
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1,8
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FORMULA
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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.
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EXAMPLE
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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).
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CROSSREFS
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A034804, A045794 (or A065678) give the terms 'b' and 'c' respectively.
Sequence in context: A050157 A054255 A063177 this_sequence A118807 A098507 A097066
Adjacent sequences: A034800 A034801 A034802 this_sequence A034804 A034805 A034806
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description, more terms, formula, etc. from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 24 2001
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