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 A176447 a(2n) = -n, a(2n+1) = 2n+1. 2
 0, 1, -1, 3, -2, 5, -3, 7, -4, 9, -5, 11, -6, 13, -7, 15, -8, 17, -9, 19, -10, 21, -11, 23, -12, 25, -13, 27, -14, 29, -15, 31, -16, 33, -17, 35, -18, 37, -19, 39, -20, 41, -21, 43, -22, 45, -23, 47, -24, 49, -25, 51, -26, 53, -27, 55, -28, 57, -29, 59, -30, 61, -31, 63, -32, 65, -33, 67, -34, 69, -35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS There is more complicated way of defining the sequence: consider the sequence of modified Bernoulli numbers EVB(n) = A176327(n)/A176289(n) and its inverse binomial transform IEVB(n) = A176328(n)/A176591(n). Then a(n) is the numerator of the difference EVB(n)-IEVB(n). The denominator of the difference is 1 if n=0, else A040001(n-1). A particularity of EVB(n) is: its (forward) binomial transform is 1, 1, 7/6, 3/2, 59/30,.. = (-1)^n*IEVB(n). Note that A026741 is related to the Rydberg-Ritz spectrum of the hydrogen atom. LINKS R. J. Mathar, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA From R. J. Mathar, Dec 01 2010:  (Start) a(n) = (-1)^n*A026741(n) = n*(1-3*(-1)^n)/4. G.f.: x*(1-x+x^2) / ( (x-1)^2*(1+x)^2 ). a(n) = +2*a(n-2) -a(n-4).  (End) a(n) = -a(-n) for all n in Z. - Michael Somos, Jun 11 2013 Euler transform of length 6 sequence [ -1, 3, 1, 0, 0, -1]. - Michael Somos, Aug 30 2014 0 = - 1 - a(n) - a(n+1) + a(n+2) + a(n+3) for all n in Z. - Michael Somos, Aug 30 2014 0 = 1 + a(n)*(-2 -a(n) + a(n+2)) - 2*a(n+1) - a(n+2) for all n in Z. - Michael Somos, Aug 30 2014 a(n) is multiplicative with a(2^e) = -(2^(e-1)) if e>0, a(p^e) = p^e otherwise. - Michael Somos, May 04 2015 G.f.: (f(x) - 3 * f(-x)) / 4 where f(x) := x / (1 - x)^2. - Michael Somos, May 04 2015 G.f.: x * (1 - x) * (1 - x^6) / ((1 - x^2)^3 * (1 - x^3)). - Michael Somos, May 04 2015 EXAMPLE G.f. = x - x^2 + 3*x^3 - 2*x^4 + 5*x^5 - 3*x^6 + 7*x^7 - 4*x^8 + 9*x^9 - 5*x^10 + ... MATHEMATICA a[n_?EvenQ]:=-(n/2); a[n_?OddQ]:=n; Table[a[n], {n, 100}] (* Alonso del Arte, Dec 01 2010 *) a[ n_] := n / If[ Mod[ n, 2] == 1, 1, -2]; (* Michael Somos, Jun 11 2013 *) CoefficientList[Series[x (1 - x + x^2)/((x - 1)^2*(1 + x)^2), {x, 0, 70}], x]  (* Michael De Vlieger, Dec 10 2016 *) LinearRecurrence[{0, 2, 0, -1}, {0, 1, -1, 3}, 80] (* Harvey P. Dale, Nov 01 2017 *) PROG (MAGMA) [n*(1-3*(-1)^n)/4: n in [0..60]]; // Vincenzo Librandi, Aug 04 2011 (PARI) {a(n) = n / if( n%2, 1, -2)}; /* Michael Somos, Jun 11 2013 */ CROSSREFS Cf. A026741. Sequence in context: A194748 A323462 A030640 * A145051 A026741 A105658 Adjacent sequences:  A176444 A176445 A176446 * A176448 A176449 A176450 KEYWORD sign,easy,mult AUTHOR Paul Curtz, Apr 18 2010 STATUS approved

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Last modified June 18 13:01 EDT 2021. Contains 345112 sequences. (Running on oeis4.)