A157615 On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding path made of alternated vertical and horizontal unitary steps.

1, 4, 7, 14, 19, 32, 39, 58, 67, 92, 103, 134, 147, 184, 199, 242, 259, 308

Offset

1,2

Comments

From an idea of Leroy Quet, discussed on the SeqFan mailing list.

David Wilson conjectures that the formula for a(n) is:

a(1)=1, then, a(n)=n^2-n+2 for n even, and a(n)=n^2-2n+4 for n>1 odd.

Links

Table of n, a(n) for n=1..18.

Giovanni Resta, Illustration of initial terms

Crossrefs

A157616, A157617

Sequence in context: A310920 A161426 A115759 * A338551 A188319 A171378

Adjacent sequences: A157612 A157613 A157614 * A157616 A157617 A157618

Keyword

hard,more,nonn,nice

Author

Giovanni Resta, Mar 03 2009

Extensions

a(13)-a(18) computed using integer linear programming by Rob Pratt, Apr 07 2015

Status

approved