A098499 Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the diagonal.

1, 5, 23, 57, 109, 169, 246, 334, 439, 555, 688, 832, 993, 1165, 1354, 1554, 1771, 1999, 2244, 2500, 2773, 3057, 3358, 3670, 3999, 4339, 4696, 5064, 5449, 5845, 6258, 6682, 7123, 7575, 8044, 8524, 9021, 9529, 10054, 10590, 11143, 11707, 12288, 12880, 13489

Offset: 0

Author

Ralf Stephan, Sep 15 2004

Keywords

• nonn
• easy

Examples

			5 squares are reachable after 1 move, from these you can reach 18 new squares more, so a(1)=5, a(2)=23.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Equals A098498(n) - A052938(n-4), n>3.

See A018836 (unbounded), A098498 (halfplane), A098500 (quadrant), A098501 (octant).

Formula

a(n) = (1/4) [28n^2 - 6n + 9 + 3(-1)^n], for n>3.

G.f.: -(3*x^7-x^6-8*x^5+4*x^4+13*x^3+13*x^2+3*x+1) / ((x-1)^3*(x+1)). - Colin Barker, Jul 14 2013

Extensions

More terms from Colin Barker, Jul 14 2013