cp's OEIS Frontend

A110331 Row sums of a number triangle related to the Pell numbers.

%I A110331 #38 Sep 08 2022 08:45:20
%S A110331 1,-1,-5,-11,-19,-29,-41,-55,-71,-89,-109,-131,-155,-181,-209,-239,
%T A110331 -271,-305,-341,-379,-419,-461,-505,-551,-599,-649,-701,-755,-811,
%U A110331 -869,-929,-991,-1055,-1121,-1189,-1259,-1331,-1405,-1481,-1559,-1639,-1721,-1805,-1891,-1979,-2069,-2161,-2255,-2351,-2449
%N A110331 Row sums of a number triangle related to the Pell numbers.
%C A110331 Row sums of A110330. Results from a general construction: the row sums of the inverse of the number triangle whose columns have e.g.f. (x^k/k!)/(1-a*x-b*x^2) have g.f. (1-(a+2)x-(2b-a-1)x^2)/(1-x)^3 and general term 1+(b-a)*n-b*n^2. This is the binomial transform of (1,-a,-2b,0,0,0,...).
%C A110331 Hankel transform of A007054(n)-2*0^n. - _Paul Barry_, Jul 20 2008
%H A110331 Vincenzo Librandi, <a href="/A110331/b110331.txt">Table of n, a(n) for n = 0..1000</a>
%H A110331 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A110331 a(n) = 1-n-n^2.
%F A110331 G.f.: (1-4*x+x^2)/(1-x)^3.
%F A110331 a(n) = binomial(n+2, 2) - 4*binomial(n+1, 2) + binomial(n, 2).
%F A110331 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 08 2012
%F A110331 E.g.f.: exp(x)*(1-2*x-x^2). - _Tom Copeland_, Dec 02 2013
%F A110331 a(n) = -A165900(n+1) (= -A028387(n-1) for n > 0). - _M. F. Hasler_, Mar 01 2014
%t A110331 CoefficientList[Series[(1-4x+x^2)/(1-x)^3,{x,0,50}],x]  (* _Vincenzo Librandi_, Jul 08 2012 *)
%t A110331 LinearRecurrence[{3,-3,1},{1,-1,-5},60] (* _Harvey P. Dale_, Mar 22 2022 *)
%o A110331 (Magma) [1-n-n^2: n in [0..50]]; // _Vincenzo Librandi_, Jul 08 2012
%o A110331 (PARI) a(n)=1-n-n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A110331 Cf. A028387 (absolute values). A165900 is another version.
%K A110331 easy,sign
%O A110331 0,3
%A A110331 _Paul Barry_, Jul 20 2005