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A098498 Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the edge. 7
1, 5, 23, 60, 110, 172, 248, 338, 442, 560, 692, 838, 998, 1172, 1360, 1562, 1778, 2008, 2252, 2510, 2782, 3068, 3368, 3682, 4010, 4352, 4708, 5078, 5462, 5860, 6272, 6698, 7138, 7592, 8060, 8542, 9038, 9548, 10072, 10610, 11162, 11728, 12308, 12902, 13510 (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 (3,-3,1).

FORMULA

a(n) = 7*n^2 - n + 2, for n>3.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>6. G.f.: -(2*x^6 -x^5 -6*x^4 +5*x^3 +11*x^2 +2*x +1) / (x -1)^3. - 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 and a(2)=23.

CROSSREFS

See A018836 (unbounded), A098499 (diagonal halfplane), A098500 (quadrant), A098501 (octant).

Sequence in context: A116581 A093622 A089137 * A159241 A179094 A176874

Adjacent sequences:  A098495 A098496 A098497 * A098499 A098500 A098501

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 September 17 12:57 EDT 2019. Contains 327131 sequences. (Running on oeis4.)