

A050187


a(n) = n * floor((n1)/2).


6



0, 0, 0, 3, 4, 10, 12, 21, 24, 36, 40, 55, 60, 78, 84, 105, 112, 136, 144, 171, 180, 210, 220, 253, 264, 300, 312, 351, 364, 406, 420, 465, 480, 528, 544, 595, 612, 666, 684, 741, 760, 820, 840, 903, 924, 990, 1012, 1081, 1104, 1176
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

T(n,2), array T as in A050186; a count of aperiodic binary words.
The Row2 triangle sums A159797 lead to the sequence given above for n >= 1 with a(1)=0. For the definitions of the Row2 and other triangle sums see A180662.  Johannes W. Meijer, May 20 2011
The number of chords joining n equally distributed points on a circle with a length less than the diameter.  Wesley Ivan Hurt, Nov 23 2013
a(n) is the maximum possible length of a circuit in the complete graph on n vertices.  Geoffrey Critzer, May 23 2014
For n > 0, a(n) is half the sum of the perimeters of the distinct rectangles that can be made with positive integer sides such that L + W = n, W < L. For example, a(14) = 84; the rectangles are 1 X 13, 2 X 12, 3 X 11, 4 X 10, 5 X 9, 6 X 8 (the 7 X 7 rectangle is not considered since we have W < L). The sum of the perimeters gives 28 + 28 + 28 + 28 + 28 + 28 = 168, half of which is 84.  Wesley Ivan Hurt, Nov 23 2017
Sum of the middle side lengths of all integersided triangles with perimeter 3n whose side lengths are in arithmetic progression (For example, when n=5 there are two triangles with perimeter 3(5) = 15 whose side lengths are in arithmetic progression: [3,5,7] and [4,5,6]; thus a(5) = 5+5 = 10).  Wesley Ivan Hurt, Nov 01 2020


LINKS

Table of n, a(n) for n=0..49.
Index entries for linear recurrences with constant coefficients, signature (1,2,2,1,1).


FORMULA

a(n) = n * floor((n1)/2).
From R. J. Mathar, Aug 08 2009: (Start)
a(n) = a(n1) + 2*a(n2)  2*a(n3)  a(n4) + a(n5).
G.f.: x^3*(3+x) / ((1+x)^2*(1x)^3). (End)
a(n) = binomial(n,2)  (n/2) * ((n+1) mod 2).  Wesley Ivan Hurt, Nov 23 2013
E.g.f.: x*(x*cosh(x) + sinh(x)*(x  1))/2.  Stefano Spezia, Nov 02 2020


MAPLE

A050187:=n>n*floor((n1)/2); seq(A050187(n), n=0..100); # Wesley Ivan Hurt, Nov 23 2013


MATHEMATICA

Table[n*Floor[(n1)/2], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 23 2013 *)


PROG

(MAGMA) [n*Floor((n1)/2): n in [0..50]]; // Wesley Ivan Hurt, May 24 2014


CROSSREFS

Cf. A050186, A159797, A180662.
Sequence in context: A325235 A135116 A259559 * A101506 A092434 A239632
Adjacent sequences: A050184 A050185 A050186 * A050188 A050189 A050190


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Dec 11 1999


EXTENSIONS

Name change by Wesley Ivan Hurt, Nov 23 2013


STATUS

approved



