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A076874 n - floor ( ( 4*n + 1 )^(1/2) ). 3

%I

%S 0,0,1,1,2,3,3,4,5,5,6,7,8,8,9,10,11,11,12,13,14,15,15,16,17,18,19,19,

%T 20,21,22,23,24,24,25,26,27,28,29,29,30,31,32,33,34,35,35,36,37,38,39,

%U 40,41,41,42,43,44,45,46,47,48,48,49,50,51,52,53,54,55,55,56,57,58,59

%N n - floor ( ( 4*n + 1 )^(1/2) ).

%C Conjecture: For n>=7, a(n)-2 is the maximum number of steps in a 2D self-avoiding random walk trapped after n steps having only 2 choices for the next step. a(n) >= A077484(n) + 2.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/stw2d.html">Results for the 2D Self-Trapping Random Walk</a>

%p A076874:=n->n - floor((4*n + 1)^(1/2)); seq(A076874(n), n=3..50); # _Wesley Ivan Hurt_, Mar 01 2014

%t Table[n - Floor[(4 n + 1)^(1/2)], {n, 3, 50}] (* _Wesley Ivan Hurt_, Mar 01 2014 *)

%Y Cf. A077483, A077484, A001411.

%K easy,nonn

%O 3,5

%A _Hugo Pfoertner_, Nov 24 2002

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Last modified August 23 11:41 EDT 2017. Contains 290995 sequences.