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A104769 Expansion of g.f. -x/(1+x-x^3).

%I A104769 #49 Oct 15 2024 08:29:09
%S A104769 0,-1,1,-1,0,1,-2,2,-1,-1,3,-4,3,0,-4,7,-7,3,4,-11,14,-10,-1,15,-25,
%T A104769 24,-9,-16,40,-49,33,7,-56,89,-82,26,63,-145,171,-108,-37,208,-316,
%U A104769 279,-71,-245,524,-595,350,174,-769,1119,-945,176,943,-1888,2064,-1121,-767,2831,-3952
%N A104769 Expansion of g.f. -x/(1+x-x^3).
%C A104769 Generating floretion is "jesright".
%C A104769 Pisano period lengths: 1, 7, 13, 14, 24, 91, 48, 28, 39, 168, 120, 182, 183, 336, 312, 56, 288, 273, 180, 168,.. (which differs from A104217 for example at index 23). - _R. J. Mathar_, Aug 10 2012
%H A104769 Michael De Vlieger, <a href="/A104769/b104769.txt">Table of n, a(n) for n = 0..10000</a>
%H A104769 Paul Barry, <a href="https://arxiv.org/abs/2104.01644">Centered polygon numbers, heptagons and nonagons, and the Robbins numbers</a>, arXiv:2104.01644 [math.CO], 2021.
%H A104769 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1).
%F A104769 a(n) = -A247917(n-1).
%F A104769 Recurrence: a(n+3) = a(n) - a(n+2); a(0) = 0, a(1) = -1, a(2) = 1.
%F A104769 a(n+1) - a(n) = ((-1)^(n+1))*a(n+5).
%F A104769 a(n) = ((-1)^n)*A050935(n+1) = ((-1)^n)*A078013(n+2).
%F A104769 a(n) = A104771(n) - A104770(n).
%t A104769 LinearRecurrence[{-1, 0, 1}, {0, -1, 1}, 61] (* or *)
%t A104769 CoefficientList[Series[-x/(1 + x - x^3), {x, 0, 60}], x] (* _Michael De Vlieger_, Jul 02 2021 *)
%o A104769 (PARI) a(n)=([0,1,0;0,0,1;1,0,-1]^n*[0;-1;1])[1,1] \\ _Charles R Greathouse IV_, Jun 11 2015
%Y A104769 Apart from signs, essentially the same as A050935 and A078013.
%Y A104769 Cf. A247917 (negative).
%Y A104769 Cf. A000931, A057597.
%K A104769 sign,easy,less
%O A104769 0,7
%A A104769 _Creighton Dement_, Mar 24 2005
%E A104769 Edited by _Ralf Stephan_, Apr 05 2009