A034804 - OEIS

%I #10 Dec 30 2023 16:54:27

%S 0,1,0,2,1,2,4,5,6,14,17,20,48,57,68,162,193,230,548,653,778,1854,

%T 2209,2632,6272,7473,8904,21218,25281,30122,71780,85525,101902,242830,

%U 289329,344732,821488,978793,1166220,2779074,3311233,3945294,9401540

%N 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 third term 'b' of these quadruples.

%F a(n)= 2*Trib(2*q) if r=0; Trib(2*q-1)+Trib(2*q+1) if r=1; Trib(2*q)+Trib(2*q+1) if r=2 where q=[(n-1)/3], r=n-1 (mod 3) and Trib denotes the tribonacci sequence (A000073) with Trib(-1)=1. G.f.: (-x^7+2*x^6-2*x^5+2*x^4-2*x^3-x)/(x^9+x^6+3*x^3-1). Recurrence: a(n)=3*a(n-3)+a(n-6)+a(n-9), n >= 10.

%e a(10)=14 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} ('b'=14 in the first 4-tuple and there is no quadruple with a+b<=c<=31 and 10 steps).

%Y A034803, A045794 (or A065678) give the terms 'a' and 'c' respectively.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

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