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A098501 Number of squares on infinite octant of chessboard at <=n knight moves from the corner. The octant includes the diagonal. 3
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

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

Sequence in context: A215215 A077278 A073683 * A180302 A116701 A068739

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

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)