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

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = 7*n^2 - n + 2 = 2*(A022264(n) + 1), for n>3.

From Colin Barker, Jul 14 2013: (Start)

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. (End)

Example

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

Mathematica

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

Crossrefs

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

Cf. A022264.

Sequence in context: A089137 A361917 A362338 * A159241 A179094 A373538

Adjacent sequences: A098495 A098496 A098497 * A098499 A098500 A098501

Keyword

nonn,easy

Author

Ralf Stephan, Sep 15 2004

Extensions

More terms from Colin Barker, Jul 14 2013

Status

approved