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 A005996 G.f.: 2(1-x^3)/((1-x)^5*(1+x)^2). (Formerly M1609) 3

%I M1609

%S 2,6,16,30,54,84,128,180,250,330,432,546,686,840,1024,1224,1458,1710,

%T 2000,2310,2662,3036,3456,3900,4394,4914,5488,6090,6750,7440,8192,

%U 8976,9826,10710,11664,12654,13718

%N G.f.: 2(1-x^3)/((1-x)^5*(1+x)^2).

%C a(n) is also the number of triples (w,x,y) having all terms in {0,...,n} and w<R<=x, where R=max(w,x,y)-min(w,x,y). [Clark Kimberling, Jun 10 2012]

%D S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Enrique Pérez Herrero, <a href="/A005996/b005996.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2*(A006918(n) + A006918(n-1) + A006918(n-2)), n>1. - Ralf Stephan, Apr 26 2003

%F a(1)=2, a(2)=6, a(3)=16, a(4)=30, a(5)=54, a(6)=84, a(n)=2*a(n-1)+a(n-2)- 4*a(n-3)+ a(n-4)+2*a(n-5)-a(n-6). - _Harvey P. Dale_, Apr 08 2013

%t Table[(1/4)*(1 + n)*(-2 + 5*n + n^2 + 2*Ceiling[1/2 - n/2] - 4*Floor[n/2]), {n, 1, 200}] (* _Enrique Pérez Herrero_, Aug 03 2012 *)

%t CoefficientList[Series[2(1-x^3)/((1-x)^5(1+x)^2),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,-4,1,2,-1},{2,6,16,30,54,84},40] (* _Harvey P. Dale_, Apr 08 2013 *)

%Y Essentially twice A034828.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_. Edited by _N. J. A. Sloane_, Aug 03 2012

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