A098500 Number of squares on infinite quarter chessboard at <=n knight moves from the corner.

1, 3, 12, 32, 59, 91, 130, 176, 229, 289, 356, 430, 511, 599, 694, 796, 905, 1021, 1144, 1274, 1411, 1555, 1706, 1864, 2029, 2201, 2380, 2566, 2759, 2959, 3166, 3380, 3601, 3829, 4064, 4306, 4555, 4811, 5074, 5344, 5621, 5905, 6196, 6494, 6799, 7111, 7430

Offset

0,2

Links

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (1/2) * (7*n^2 + n + 2), for n>3.

G.f.: -(2*x^6-2*x^5-4*x^4+4*x^3+6*x^2+1) / (x-1)^3. - Colin Barker, Jul 15 2013

Example

3 squares are reachable after 1 move, from these you can reach 8 new squares more, so a(1)=3, a(2)=12.

Crossrefs

First differences are in A047883.

See A018836 (unbounded), A098498 (halfplane), A098499 (diagonal halfplane), A098501 (octant).

Sequence in context: A037237 A005718 A199231 * A037236 A309693 A365738

Adjacent sequences: A098497 A098498 A098499 * A098501 A098502 A098503

Keyword

nonn,easy

Author

Ralf Stephan, Sep 15 2004

Extensions

More terms from Colin Barker, Jul 15 2013

Status

approved