A018840 Number of steps for {2,3} fairy knight to reach (n,0) on infinite chessboard.

0, 5, 4, 5, 2, 5, 2, 5, 4, 5, 4, 7, 4, 5, 6, 7, 6, 7, 6, 7, 8, 9, 8, 9, 8, 9, 10, 11, 10, 11, 10, 11, 12, 13, 12, 13, 12, 13, 14, 15, 14, 15, 14, 15, 16, 17, 16, 17, 16, 17, 18, 19, 18, 19, 18, 19, 20, 21, 20, 21, 20, 21, 22, 23, 22, 23, 22, 23, 24, 25, 24, 25, 24, 25, 26, 27, 26, 27, 26, 27

Offset

0,2

Comments

This piece is also known as a (2,3)-leaper or a zebra. - Franklin T. Adams-Watters, Dec 27 2017

Apparently also the minimum number of moves of the (1,5)-leaper to reach (n,n) starting from (0,0). - R. J. Mathar, Jan 05 2018

Links

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

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

Formula

For n >= 18, a(n) = a(n-6) + 2. - David W. Wilson

From Colin Barker, Dec 28 2017: (Start)

G.f.: x*(5 - x + x^2 - 3*x^3 + 3*x^4 - 3*x^5 - 2*x^6 + 2*x^9 - 2*x^12 + 2*x^13 - 2*x^16 + 2*x^17) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

(End)

3*a(n) = A004442(n+3)-A084100(n), n>11. - R. J. Mathar, Jan 02 2018

Prog

(PARI) concat(0, Vec(x*(5 - x + x^2 - 3*x^3 + 3*x^4 - 3*x^5 - 2*x^6 + 2*x^9 - 2*x^12 + 2*x^13 - 2*x^16 + 2*x^17) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)) + O(x^100))) \\ Colin Barker, Dec 28 2017

Crossrefs

Sequence in context: A337029 A293557 A123587 * A058209 A160789 A266111

Adjacent sequences: A018837 A018838 A018839 * A018841 A018842 A018843

Keyword

nonn,easy

Author

Marc LeBrun

Status

approved