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A104161 G.f.: x*(1 - x + x^2)/((1-x)^2 * (1 - x - x^2)). 16

%I

%S 0,1,2,5,10,19,34,59,100,167,276,453,740,1205,1958,3177,5150,8343,

%T 13510,21871,35400,57291,92712,150025,242760,392809,635594,1028429,

%U 1664050,2692507,4356586,7049123

%N G.f.: x*(1 - x + x^2)/((1-x)^2 * (1 - x - x^2)).

%C A floretion-generated sequence.

%C Partial sums of Leonardo numbers A001595. - _Jonathan Vos Post_, Jan 01 2011

%H G. C. Greubel, <a href="/A104161/b104161.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

%F Superseeker results (incomplete): a(2) - 2a(n+1) + a(n) = A006355(n+1) (Number of binary vectors of length n containing no singletons); a(n+1) - a(n) = A001595(n) (2-ranks of difference sets constructed from Segre hyperovals); a(n) + n + 1 = A001595(n+1).

%F A107909(a(n)) = A000975(n). - _Reinhard Zumkeller_, May 28 2005

%F From _Ross La Haye_, Aug 03 2005: (Start)

%F a(n) = 2*(Fibonacci(n+2) - 1) - n.

%F a(n) =Ssum_{k=0..n} A101220(n-k, 0, k). (End)

%F From _Gary W. Adamson_, Apr 02 2006: (Start)

%F a(n) = a(n-1) + a(n-2) + n-1.

%F a(n) = row sums of A117915, starting (1, 2, 5, 10...). (End)

%F a(n) = Sum_{k=0..n} A109754(n-k,k). - _Ross La Haye_, Apr 12 2006

%F a(n) = (Sum_{k=0..n} (n-k)Fibonacci(k-1) + Fibonacci(k)) - n. - _Ross La Haye_, May 31 2006

%F From _R. J. Mathar_, Apr 18 2008: (Start)

%F a(n) = -2 - n + (-A094214)^n*(1-A010499/5) + (1+A010499/5)/A094214^n.

%F a(n) = A006355(n+3) - n - 2. (End)

%F a(0)=0, a(1)=1, a(2)=2, a(3)=5, a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4). - _Harvey P. Dale_, Sep 06 2012

%t a=0;b=1;Table[c=b+a+n; a=b; b=c, {n,-1,80}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 21 2011 *)

%t CoefficientList[Series[x*(1-x+x^2)/((1-x)^2*(1-x-x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{3,-2,-1,1},{0,1,2,5},40] (* _Harvey P. Dale_, Sep 06 2012 *)

%o Floretion Algebra Multiplication Program, FAMP Code: 1vesrokseq[ (- .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e)('i + i' + 'ji' + 'ki' + e) ] RokType: Y[sqa.Findk()] = Y[sqa.Findk()] + p.

%o (PARI) x='x+O('x^50); concat(0, Vec(x*(1-x+x^2)/((1-x)^2*(1-x-x^2)))) \\ _G. C. Greubel_, Sep 26 2017

%Y Cf. A006355, A001595, A145912.

%K easy,nonn

%O 0,3

%A _Creighton Dement_, Mar 10 2005

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Last modified November 17 00:02 EST 2018. Contains 317275 sequences. (Running on oeis4.)