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%I #19 Jul 26 2016 20:48:10
%S 0,-1,8,-22,48,-87,144,-220,320,-445,600,-786,1008,-1267,1568,-1912,
%T 2304,-2745,3240,-3790,4400,-5071,5808,-6612,7488,-8437,9464,-10570,
%U 11760,-13035,14400,-15856,17408,-19057,20808,-22662,24624,-26695,28880,-31180,33600
%N Alternating sum of octagonal pyramidal numbers.
%H OEIS Wiki, <a href="http://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-2,2,3,1).
%F G.f.: x*(1 - 5*x)/((x - 1)*(x + 1)^4).
%F a(n) = ((2*n^3 + 4*n^2 - 1)*(-1)^n + 1)/4.
%F a(n) = Sum_{k = 0..n} (-1)^k*A002414(k).
%F Sum_{n>=1} 1/a(n) = -0.906890389180715042293808708467278316660747358... . - _Vaclav Kotesovec_, Feb 26 2016
%t Table[((2 n^3 + 4 n^2 - 1) (-1)^n + 1)/4, {n, 0, 40}]
%t LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 8, -22, 48}, 41]
%o (PARI) a(n)=(2*n^3 + 4*n^2 - 1)*(-1)^n\/4 \\ _Charles R Greathouse IV_, Jul 26 2016
%Y Cf. A000292, A002414, A002717, A173196, A266677.
%K sign,easy
%O 0,3
%A _Ilya Gutkovskiy_, Feb 26 2016
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