A018841 Number of steps for {2,3} fairy knight to reach (n,n) on infinite chessboard.

0, 2, 4, 6, 4, 2, 4, 6, 6, 6, 4, 6, 6, 6, 8, 6, 8, 8, 8, 10, 8, 10, 10, 10, 12, 10, 12, 12, 12, 14, 12, 14, 14, 14, 16, 14, 16, 16, 16, 18, 16, 18, 18, 18, 20, 18, 20, 20, 20, 22, 20, 22, 22, 22, 24, 22, 24, 24, 24, 26, 24, 26, 26, 26, 28, 26, 28, 28, 28, 30, 28, 30, 30, 30, 32, 30, 32, 32

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

For n >= 14, a(n) = a(n-5) + 2. - David W. Wilson

From Colin Barker, Jan 04 2018: (Start)

G.f.: 2*x*(1 + x + x^2 - x^3 - x^4 - x^7 + x^8 - x^11 + x^13) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-5) - a(n-6) for n>5.

(End)

Prog

(PARI) concat(0, Vec(2*x*(1 + x + x^2 - x^3 - x^4 - x^7 + x^8 - x^11 + x^13) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Jan 04 2018

Crossrefs

Sequence in context: A367198 A317310 A231655 * A182043 A337937 A138125

Adjacent sequences: A018838 A018839 A018840 * A018842 A018843 A018844

Keyword

nonn,easy

Author

Marc LeBrun

Status

approved