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A060423 Number of obtuse triangles made from vertices of a regular n-gon. 2
0, 0, 0, 0, 0, 5, 6, 21, 24, 54, 60, 110, 120, 195, 210, 315, 336, 476, 504, 684, 720, 945, 990, 1265, 1320, 1650, 1716, 2106, 2184, 2639, 2730, 3255, 3360, 3960, 4080, 4760, 4896, 5661, 5814, 6669, 6840, 7790, 7980, 9030, 9240, 10395, 10626 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..46.

FORMULA

a(n) = n*(n-1)*(n-3)/8 when n odd; n*(n-2)*(n-4)/8 when n even.

G.f.: x^5*(x+5)/((1-x)(1-x^2)^3). - Michael Somos, Jan 30 2004

For n odd, a(n) = A080838(n). - Gerald McGarvey, Sep 14 2008

a(n) = n*(2*n-3-(-1)^n)*(2*n-7-(-1)^n)/32. - Wesley Ivan Hurt, Dec 31 2013

MAPLE

A060423:=n->n*(2*n-3-(-1)^n)*(2*n-7-(-1)^n)/32; seq(A060423(n), n=0..100); # Wesley Ivan Hurt, Dec 31 2013

MATHEMATICA

Table[n(2n-3-(-1)^n)(2n-7-(-1)^n)/32, {n, 0, 100}] (* Wesley Ivan Hurt, Dec 31 2013 *)

Table[If[EvenQ[n], (n(n-2)(n-4))/8, (n(n-1)(n-3))/8], {n, 0, 50}] (* Harvey P. Dale, Sep 18 2018 *)

PROG

(PARI) a(n)=polcoeff(x^5*(5+x)/(1-x)/(1-x^2)^3+x*O(x^n), n)

(MAGMA) [n*(2*n-3-(-1)^n)*(2*n-7-(-1)^n)/32 : n in [0..60]]; // Wesley Ivan Hurt, Apr 14 2017

CROSSREFS

Cf. A000330, A007290, A046092.

Sequence in context: A231181 A259775 A057520 * A037951 A095308 A132796

Adjacent sequences:  A060420 A060421 A060422 * A060424 A060425 A060426

KEYWORD

easy,nice,nonn

AUTHOR

Sen-Peng Eu, Apr 05 2001

STATUS

approved

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Last modified July 21 19:51 EDT 2019. Contains 325199 sequences. (Running on oeis4.)