A098501 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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