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

Author

Ralf Stephan, Sep 15 2004

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

First differences are in A047883.

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

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

Extensions

More terms from Colin Barker, Jul 15 2013