A098501 Number of squares on infinite octant of chessboard at <=n knight moves from the corner. The octant includes the diagonal.

1, 2, 5, 13, 31, 49, 70, 93, 121, 151, 186, 223, 265, 309, 358, 409, 465, 523, 586, 651, 721, 793, 870, 949, 1033, 1119, 1210, 1303, 1401, 1501, 1606, 1713, 1825, 1939, 2058, 2179, 2305, 2433, 2566, 2701, 2841, 2983, 3130, 3279, 3433, 3589, 3750, 3913, 4081

Offset: 0

Author

Ralf Stephan, Sep 15 2004

Keywords

• nonn
• easy

Examples

			2 squares are reachable after 1 move, from these you can reach 3 new squares more, so a(1)=2, a(2)=5.
		

Links

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

Crossrefs

See A018836 (unbounded), A098498 (halfplane), A098499 (diagonal halfplane), A098500 (quadrant).

Formula

a(n) = (1/8) * [14n^2 + 8n + 5 + 3(-1)^n], for n>4.

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

Extensions

More terms from Colin Barker, Jul 14 2013