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 A182228 a(n) = 3*a(n-2) - a(n-1) for n > 1, a(0) = 0, a(1) = 1. 3
 0, 1, -1, 4, -7, 19, -40, 97, -217, 508, -1159, 2683, -6160, 14209, -32689, 75316, -173383, 399331, -919480, 2117473, -4875913, 11228332, -25856071, 59541067, -137109280, 315732481, -727060321, 1674257764, -3855438727, 8878212019, -20444528200, 47079164257, -108412748857 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This is A006130 with minus signs on every other term. - T. D. Noe, Apr 23 2012 LINKS G. C. Greubel, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (-1,3). FORMULA From R. J. Mathar, Apr 22 2013: (Start) a(n) = -A140167(n). G.f.: x/(1 + x - 3*x^2). (End) G.f.: 1 - Q(0), where Q(k) = 1 + 3*x^2 - (k+2)*x + x*(k+1 - 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 06 2013 E.g.f.: (-1/sqrt(13))*(exp(-(1+sqrt(13))*x/2) - exp(-(1-sqrt(13))*x/2)). - G. C. Greubel, Aug 30 2015 a(n) = (-(-1)^n/sqrt(13))*(((1 + sqrt(13))/2)^n - ((1 - sqrt(13))/2)^n). - Taras Goy, Jul 17 2018 MATHEMATICA RecurrenceTable[{a[n]== - a[n-1] + 3*a[n-2], a[0]== 0, a[1]== 1}, a, {n, 0, 200}] (* G. C. Greubel, Aug 30 2015 *) LinearRecurrence[{-1, 3}, {0, 1}, 40] (* Harvey P. Dale, Oct 23 2016 *) PROG (Python) prpr = 0 prev = 1 for i in range(2, 55): . current = prpr*3-prev . print current, . prpr = prev . prev = current (MAGMA) [n le 2 select n-1 else -Self(n-1) + 3*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 31 2015 CROSSREFS Cf. A140167. Sequence in context: A323105 A006130 A140167 * A182646 A190646 A220011 Adjacent sequences:  A182225 A182226 A182227 * A182229 A182230 A182231 KEYWORD sign,easy AUTHOR Alex Ratushnyak, Apr 19 2012 STATUS approved

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Last modified October 23 09:24 EDT 2019. Contains 328345 sequences. (Running on oeis4.)