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

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, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 53, 54, 55, 55, 56, 57, 58, 59

Offset: 3

Author

Hugo Pfoertner, Nov 24 2002

Keywords

• easy
• nonn

Comments

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.

Links

• Hugo Pfoertner, Results for the 2D Self-Trapping Random Walk

Crossrefs

Cf. A077483, A077484, A001411.

Programs

Maple

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

Mathematica

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