login
A123919
Number of numbers congruent to 2 or 4 mod 6 and <= n.
3
0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 26
OFFSET
1,4
COMMENTS
First differences of A056827. - R. J. Mathar, Nov 22 2008
a(n+2) is the graph radius of the n X n knight graph for n > 7. - Eric W. Weisstein, Nov 20 2019
LINKS
Eric Weisstein's World of Mathematics, Graph Radius
Eric Weisstein's World of Mathematics, Knight Graph
FORMULA
a(n) = floor(n/2) - floor(n/6).
From R. J. Mathar, Nov 22 2008: (Start)
G.f.: x^2*(1+x^2)/((1+x)*(1-x)^2*(1+x+x^2)*(1-x+x^2)).
a(n+1) - a(n) = A120325(n+1). (End)
a(n) = A004526(n) - A152467(n). - Omar E. Pol, Nov 25 2019
a(n) = a(n-1)+a(n-6)-a(n-7). - Wesley Ivan Hurt, Apr 26 2021
MATHEMATICA
a[n_] := Floor[n/2] - Floor[n/6]; Array[a, 80] (* Robert G. Wilson v Oct 29 2006 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 1, 2, 2, 2, 2}, 80] (* G. C. Greubel, Aug 07 2019 *)
PROG
(PARI) my(x='x+O('x^80)); concat([0], Vec(x^2*(1+x^2)/((1-x)*(1-x^6)))) \\ G. C. Greubel, Aug 07 2019
(PARI) a(n) = floor(n/2) - floor(n/6); \\ Joerg Arndt, Nov 23 2019
(GAP) a:=[0, 1, 1, 2, 2, 2, 2];; for n in [8..80] do a[n]:=a[n-1]+a[n-6]-a[n-7]; od; a; # G. C. Greubel, Aug 07 2019
(Magma) [Floor(n/2) - Floor(n/6) : n in [1..100]]; // Wesley Ivan Hurt, Apr 26 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Oct 29 2006
STATUS
approved