A098498 Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the edge.

1, 5, 23, 60, 110, 172, 248, 338, 442, 560, 692, 838, 998, 1172, 1360, 1562, 1778, 2008, 2252, 2510, 2782, 3068, 3368, 3682, 4010, 4352, 4708, 5078, 5462, 5860, 6272, 6698, 7138, 7592, 8060, 8542, 9038, 9548, 10072, 10610, 11162, 11728, 12308, 12902, 13510

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 and a(2)=23.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

See A018836 (unbounded), A098499 (diagonal halfplane), A098500 (quadrant), A098501 (octant).

Programs

Mathematica

LinearRecurrence[{3, -3, 1}, {1, 5, 23, 60, 110, 172, 248}, 50] (* Paolo Xausa, Jul 17 2024 *)

Formula

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

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>6. G.f.: -(2*x^6 -x^5 -6*x^4 +5*x^3 +11*x^2 +2*x +1) / (x -1)^3. - Colin Barker, Jul 14 2013

Extensions

More terms from Colin Barker, Jul 14 2013