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A098499 Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the diagonal. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A053664 A186030 A092544 * 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

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Last modified August 20 11:27 EDT 2017. Contains 290835 sequences.