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A060423
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Number of obtuse triangles made from vertices of a regular n-gon.
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2
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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
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OFFSET
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0,6
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LINKS
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FORMULA
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a(n) = n*(n-1)*(n-3)/8 when n odd; n*(n-2)*(n-4)/8 when n even.
E.g.f.: x*((x - 3)*x*cosh(x) + (x^2 - x + 3)*sinh(x))/8. - Stefano Spezia, May 28 2022
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MAPLE
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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STATUS
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approved
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