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%I M1577 #37 Jul 14 2023 14:23:16
%S 1,2,6,11,23,38,64,95,141,194,266,347,451,566,708,863,1049,1250,1486,
%T 1739,2031,2342,2696,3071,3493,3938,4434,4955,5531,6134,6796,7487,
%U 8241,9026,9878,10763,11719,12710,13776,14879,16061,17282,18586,19931,21363,22838,24404,26015,27721,29474,31326,33227,35231,37286
%N Number of paraffins.
%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="/A005999/b005999.txt">Table of n, a(n) for n = 1..5000</a>
%H S. M. Losanitsch, <a href="http://dx.doi.org/10.1002/cber.189703002144">Die Isomerie-Arten bei den Homologen der Paraffin-Reihe</a>, Chem. Ber. 30 (1897), 1917-1926.
%H S. M. Losanitsch, <a href="/A000602/a000602_1.pdf">Die Isomerie-Arten bei den Homologen der Paraffin-Reihe</a>, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).
%F G.f.: (x^5+2*x^4+x^3+x^2+1)/((-1+x)^2*(-1+x^2)^2).
%F a(n) = A005997(n) - (n-1)^2. - _Enrique Pérez Herrero_, Mar 28 2012
%p A005999:=n->1+floor((n-1)/2)+2*(binomial(n+1,3)-binomial(floor((n+1)/2),3)-binomial(ceil((n+1)/2),3))-(n-1)^2: seq(A005999(n), n=1..40); # _Wesley Ivan Hurt_, Sep 16 2014
%t A005997[n_] := 1 + Floor[(n-1)/2] + 2*(Binomial[n+1,3] -Binomial[Floor[(n+1)/2],3] - Binomial[Ceiling[(n+1)/2],3]); A005999[n_] := A005997[n] - (n-1)^2; Array[A005999, 100] (* _Enrique Pérez Herrero_, Apr 22 2012 *)
%o (Magma) [1+Floor((n-1)/2)+2*(Binomial(n+1,3)-Binomial(Floor((n+1)/2),3)-Binomial(Ceiling((n+1)/2),3))-(n-1)^2 : n in [1..50]]; // _Wesley Ivan Hurt_, Sep 16 2014
%o (PARI) Vec( (x^5+2*x^4+x^3+x^2+1)/(-1+x)^2/(-1+x^2)^2 + O(x^66) ) \\ _Joerg Arndt_, Sep 16 2014
%Y Cf. A005997.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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