3,2

Jean Meeus, Wiskunde Post (Belgium), Vol. 10, 1972, pp. 62-63.

C. A. Pickover, The Mathematics of Oz, Problem 58 "The Beauty of Polygon Slicing", Cambridge University Press, 2002.

T. D. Noe, Table of n, a(n) for n=3..1000

Sascha Kurz, m-gons in regular n-gons

B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.

B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).

B. Poonen & M. Rubinstein, The Number Of Intersection Points Made By The Diagonals Of A Regular Polygon, SIAM Journal on Discrete Mathematics, pp. 135-6 vol. 11 no.1 1998.

B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, arXiv version, which has fewer typos than the SIAM version.

B. Poonen and M. Rubinstein, Mathematica programs for these sequences

Eric Weisstein's World of Mathematics, Regular Polygon Division by Diagonals

Sequences formed by drawing all diagonals in regular polygon

For odd n>3, a(n) = sumstep {i=5, n, 2, (i-2)*floor(n/2)+(i-4)*ceil(n/2)+1} + x*(x+1)*(2*x+1)/6*n), where x=(n-5)/2. Simplifying the floor/ceil components gives the Pari code below. - Jon Perry (perry(AT)globalnet.co.uk), Jul 08 2003

Simpler formula for odd n, n>=3: (24 - 42n + 23n^2 - 6n^3 + n^4)/24. - Graeme McRae (g_m(AT)mcraefamily.com), Dec 24 2004

a(n)=A006533(n)-n. - T. D. Noe, Dec 23 2006

del[m_, n_]:=If[Mod[n, m]==0, 1, 0]; R[n_]:=If[n<3, 0, (n^4-6n^3+23n^2-42n+24)/24 + del[2, n](-5n^3+42n^2-40n-48)/48 - del[4, n](3n/4) + del[6, n](-53n^2+310n)/12 + del[12, n](49n/2) + del[18, n]*32n + del[24, n]*19n - del[30, n]*36n - del[42, n]*50n - del[60, n]*190n - del[84, n]*78n - del[90, n]*48n - del[120, n]*78n - del[210, n]*48n]; Table[R[n], {n, 1, 1000}] - T. D. Noe (noe(AT)sspectra.com), Dec 21 2006

(PARI) { a(n)=local(nr, x, fn, cn, fn2); nr=0; fn=floor(n/2); cn=ceil(n/2); fn2=(fn-1)^2-1; nr=fn2*n+fn+(n-2)*fn+cn; x=(n-5)/2; if (x>0, nr+=x*(x+1)*(2*x+1)/6*n); nr; }

Sequences related to chords in a circle: A001006, A054726, A006533, A006561, A006600, A007569, A007678. See also entries for chord diagrams in Index file.

Adjacent sequences: A007675 A007676 A007677 this_sequence A007679 A007680 A007681

Sequence in context: A006527 A057304 A001752 this_sequence A115294 A110610 A051462

easy,nonn,nice

njas, Bjorn Poonen (poonen(AT)math.princeton.edu)

More terms from Graeme McRae (g_m(AT)mcraefamily.com), Dec 26 2004