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

0,2

Links

Table of n, a(n) for n=0..44.

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

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

Example

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

Crossrefs

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

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

Sequence in context: A186030 A092544 A319087 * A075565 A075707 A126420

Adjacent sequences: A098496 A098497 A098498 * A098500 A098501 A098502

Keyword

nonn,easy

Author

Ralf Stephan, Sep 15 2004

Extensions

More terms from Colin Barker, Jul 14 2013

Status

approved