

A047878


a(n)=least number of knight's moves from corner (0,0) to nth diagonal of unbounded chessboard.


1



0, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 15, 14, 15, 16, 15, 16, 17, 16, 17, 18, 17, 18, 19, 18, 19, 20, 19, 20, 21, 20, 21, 22, 21, 22, 23, 22, 23, 24, 23, 24, 25
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OFFSET

0,2


COMMENTS

a(n)=MIN{T(i,ni): i=0,1,...,n}, array T as in A049604.
Apart from initial terms, same as A008611.  Anton Chupin, Oct 24 2009


LINKS

Table of n, a(n) for n=0..71.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).


FORMULA

a(3n)=n, a(3n+1)=n+1, a(3n+2)=n+2 for n >= 1.
a(n)=a(n1)+a(n3)a(n4) for n>5. G.f.: x*(2*x^42*x^3x^2x+3) / ((x1)^2*(x^2+x+1)).  Colin Barker, May 04 2014


MATHEMATICA

LinearRecurrence[{1, 0, 1, 1}, {0, 3, 2, 1, 2, 3}, 80] (* Harvey P. Dale, Sep 01 2018 *)


PROG

(PARI) concat(0, Vec(x*(2*x^42*x^3x^2x+3)/((x1)^2*(x^2+x+1)) + O(x^100))) \\ Colin Barker, May 04 2014


CROSSREFS

Sequence in context: A174543 A260450 A036583 * A324782 A256427 A120441
Adjacent sequences: A047875 A047876 A047877 * A047879 A047880 A047881


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling


STATUS

approved



