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A210673 a(n) = a(n-1)+a(n-2)+n-4, a(0)=0, a(1)=1.

%I A210673 #35 Aug 21 2016 12:04:59
%S A210673 0,1,-1,-1,-2,-2,-2,-1,1,5,12,24,44,77,131,219,362,594,970,1579,2565,
%T A210673 4161,6744,10924,17688,28633,46343,74999,121366,196390,317782,514199,
%U A210673 832009,1346237,2178276,3524544,5702852,9227429,14930315,24157779,39088130,63245946
%N A210673 a(n) = a(n-1)+a(n-2)+n-4, a(0)=0, a(1)=1.
%C A210673 Second differences are Fibonacci numbers A000045 with offset -4. - _Olivier Gérard_, Aug 21 2016
%H A210673 Harvey P. Dale, <a href="/A210673/b210673.txt">Table of n, a(n) for n = 0..1000</a>
%H A210673 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).
%F A210673 a(0)=0, a(1)=1, a(2)=-1, a(3)=-1, a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). - _Harvey P. Dale_, Oct 03 2012
%F A210673 G.f.: x/Q(0), where Q(k)= 1 + (k+1)*x/(1 - x - x*(1-x)/(x + (k+1)*(1-x)/Q(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Apr 24 2013
%F A210673 G.f.: -x*(2*x-1)^2 / ((x-1)^2*(x^2+x-1)). - _Colin Barker_, May 31 2013
%t A210673 RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-1]+a[n-2]+n-4},a,{n,50}] (* or *) LinearRecurrence[{3,-2,-1,1},{0,1,-1,-1},50] (* _Harvey P. Dale_, Oct 03 2012 *)
%Y A210673 Cf. A066982: a(n)=a(n-1)+a(n-2)+n-2, a(0)=0, a(1)=1 (except the first term).
%Y A210673 Cf. A104161: a(n)=a(n-1)+a(n-2)+n-1, a(0)=0, a(1)=1.
%Y A210673 Cf. A001924: a(n)=a(n-1)+a(n-2)+n,   a(0)=0, a(1)=1.
%Y A210673 Cf. A192760: a(n)=a(n-1)+a(n-2)+n+1, a(0)=0, a(1)=1.
%Y A210673 Cf. A192761: a(n)=a(n-1)+a(n-2)+n+2, a(0)=0, a(1)=1.
%Y A210673 Cf. A192762: a(n)=a(n-1)+a(n-2)+n+3, a(0)=0, a(1)=1.
%Y A210673 Cf. A210675: a(n)=a(n-1)+a(n-2)+n+4, a(0)=0, a(1)=1.
%K A210673 sign,easy
%O A210673 0,5
%A A210673 _Alex Ratushnyak_, May 09 2012