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A018842 Number of squares on infinite chessboard at n knight's moves from center. 3
1, 8, 32, 68, 96, 120, 148, 176, 204, 232, 260, 288, 316, 344, 372, 400, 428, 456, 484, 512, 540, 568, 596, 624, 652, 680, 708, 736, 764, 792, 820, 848, 876, 904, 932, 960, 988, 1016, 1044, 1072, 1100, 1128, 1156 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Duchin, Moon. "Counting in Groups: Fine Asymptotic Geometry." Notices of the AMS 63.8 (2016), pp. 871-974.  See p. 873.

LINKS

Table of n, a(n) for n=0..42.

Mordechai Katzman, Knight's moves on an infinite board

M. Katzman, Counting Monomials, J. Alg. Comb. 22 (2005) 331-341

A. M. Miller and D. L. Farnsworth, Counting the Number of Squares Reachable in k Knight's Moves, Open Journal of Discrete Mathematics, 2013, 3, 151-154

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

FORMULA

a(n) = 28*n-20, n >= 5.

G.f.: (1 + 5*x + 12*x^2 - 8*x^4 + 4*x^5)*(1+x)/(1-x)^2.

MAPLE

(1 + 5*x + 12*x^2 - 8*x^4 + 4*x^5)*(1+x)/(1-x)^2; seq(coeff(series(%, x, n+1), x, n), n=0..50);

MATHEMATICA

CoefficientList[Series[(1+5x+12x^2-8x^4+4x^5)(1+x)/(1-x)^2, {x, 0, 50}], x] (* or *) Join[{1, 8, 32, 68, 96}, LinearRecurrence[{2, -1}, {120, 148}, 46]] (* Harvey P. Dale, Jul 05 2011 *)

CROSSREFS

Cf. A018836 (partial sums), A038522.

Sequence in context: A253295 A290960 A009245 * A139098 A224543 A211633

Adjacent sequences:  A018839 A018840 A018841 * A018843 A018844 A018845

KEYWORD

nonn,nice,walk,easy

AUTHOR

N. J. A. Sloane, Marc LeBrun

EXTENSIONS

Formula corrected by Jean Drabbe, Mar 11 2013

STATUS

approved

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Last modified November 19 08:40 EST 2018. Contains 317347 sequences. (Running on oeis4.)