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

0,2

Links

Table of n, a(n) for n=0..48.

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

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

Example

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

Crossrefs

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

Sequence in context: A215215 A077278 A073683 * A363513 A180302 A116701

Adjacent sequences: A098498 A098499 A098500 * A098502 A098503 A098504

Keyword

nonn,easy

Author

Ralf Stephan, Sep 15 2004

Extensions

More terms from Colin Barker, Jul 14 2013

Status

approved