cp's OEIS Frontend

A139482 Binomial transform of [1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, ...].

%I A139482 #25 Aug 23 2018 02:10:56
%S A139482 1,2,5,11,20,32,47,65,86,110,137,167,200,236,275,317,362,410,461,515,
%T A139482 572,632,695,761,830,902,977,1055,1136,1220,1307,1397,1490,1586,1685,
%U A139482 1787,1892,2000,2111,2225
%N A139482 Binomial transform of [1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, ...].
%C A139482 A007318 * [1, 1, 2, 1, -1, 1, -1, 1, ...].
%C A139482 The quadratic expression for a(n) follows at once by taking into account that the alternate row sums in the Pascal triangle are equal to zero (starting with the second row). - _Emeric Deutsch_, May 03 2008
%C A139482 For n > 1, 3*(8*a(n) - 13) = A016945(n-2)^2. - _Vincenzo Librandi_, Feb 15 2012
%H A139482 Vincenzo Librandi, <a href="/A139482/b139482.txt">Table of n, a(n) for n = 1..1000</a>
%H A139482 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A139482 G.f.: (x^3+2*x^2-x+1)/(-x^3+3*x^2-3*x+1). - _Alexander R. Povolotsky_, Apr 24 2008
%F A139482 a(n) = (10 - 9*n + 3*n^2)/2 for n >= 2. - _Emeric Deutsch_, May 03 2008
%F A139482 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=2, a(3)=5, a(4)=11. - _Harvey P. Dale_, May 02 2015
%e A139482 a(4) = 11 = (1, 3, 3, 1) dot (1, 1, 2, 1) = (1 + 3 + 6 + 1).
%p A139482 1,seq((10+3*n^2-9*n)*1/2,n=2..40); # _Emeric Deutsch_, May 03 2008
%t A139482 Join[{1,2},FoldList[##+3&,5,3*Range@100]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)
%t A139482 LinearRecurrence[{3,-3,1},{1,2,5,11},40] (* _Harvey P. Dale_, May 02 2015 *)
%K A139482 nonn,easy
%O A139482 1,2
%A A139482 _Gary W. Adamson_, Apr 23 2008
%E A139482 More terms from _Emeric Deutsch_, May 03 2008