This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A211379 Number of pairs of parallel diagonals in a regular n-gon. 1
 0, 0, 0, 3, 7, 16, 27, 45, 66, 96, 130, 175, 225, 288, 357, 441, 532, 640, 756, 891, 1035, 1200, 1375, 1573, 1782, 2016, 2262, 2535, 2821, 3136, 3465, 3825, 4200, 4608, 5032, 5491, 5967, 6480, 7011, 7581, 8170, 8800, 9450, 10143, 10857, 11616, 12397, 13225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,4 LINKS Eric Weisstein, Regular Polygon Division by Diagonals (MathWorld). Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA a(n) = 1/2*n*(binomial(1/2*(n-2),2)+binomial(1/2*(n-4),2)) = 1/8*n*(n-4)^2 for n even; a(n) = n*binomial(1/2*(n-3),2) = 1/8*n*(n-3)*(n-5) for n odd. G.f.: -x^6*(x^2-x-3) / ((x-1)^4*(x+1)^2). [Colin Barker, Feb 14 2013] EXAMPLE a(6) = 3 since by numbering the vertices from 1 to 6 there are three pairs of parallel diagonals, i. e. {[1, 3], [4, 6]}, {[1, 5], [2, 4]}, {[2, 6], [3, 5]}. a(7) = 7 since there are the seven pairs {[1, 3], [4, 7]}, {[1, 4], [5, 7]}, {[1, 5], [2, 4]}, {[1, 6], [2, 5]}, {[2, 6], [3, 5]}, {[2, 7], [3, 6]}, {[3, 7], [4, 6]}. a(8) = 16 since there are the sixteen pairs {[1, 3], [4, 8]}, {[1, 3], [5, 7]}, {[1, 4], [5, 8]}, {[1, 5], [2, 4]}, {[1, 5], [6, 8]}, {[1, 6], [2, 5]}, {[1, 7], [2, 6]}, {[1, 7], [3, 5]}, {[2, 4], [6, 8]}, {[2, 6], [3, 5]}, {[2, 7], [3, 6]}, {[2, 8], [3, 7]}, {[2, 8], [4, 6]}, {[3, 7], [4, 6]}, {[3, 8], [4, 7]}, {[4, 8], [5, 7]}. MAPLE a:=n->piecewise(n mod 2 = 0, 1/8*n*(n-4)^2, n mod 2 = 1, 1/8*n*(n-3)*(n-5), 0); CROSSREFS Cf. A000096. Sequence in context: A036666 A218359 A117491 * A213180 A110585 A184677 Adjacent sequences:  A211376 A211377 A211378 * A211380 A211381 A211382 KEYWORD nonn,easy AUTHOR Martin Renner, Feb 07 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)