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 A005998 Number of paraffins. (Formerly M1740) 1
 1, 2, 7, 14, 29, 48, 79, 116, 169, 230, 311, 402, 517, 644, 799, 968, 1169, 1386, 1639, 1910, 2221, 2552, 2927, 3324, 3769, 4238, 4759, 5306, 5909, 6540, 7231, 7952, 8737, 9554, 10439, 11358, 12349, 13376, 14479, 15620, 16841, 18102, 19447, 20834, 22309 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 F. Javier de Vega, An extension of Furstenberg's theorem of the infinitude of primes, arXiv:2003.13378 [math.NT], 2020. S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy) FORMULA G.f.: x*(x^4+2*x^3+2*x^2+1)/(-1+x)^2/(-1+x^2)^2. MAPLE a:= n-> (Matrix([[0, -1, -4, -11, -22, -41]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -4, 1, 2, -1][i] else 0 fi)^n)[1, 1]: seq(a(n), n=1..38); # Alois P. Heinz, Jul 31 2008 MATHEMATICA a[n_] := 1/8*(2*n^3-2*n^2+5*n-(-1)^n*(n+1)+1); Array[a, 40] (* Jean-François Alcover, Mar 13 2014 *) CoefficientList[Series[(x^4 + 2 x^3 + 2 x^2 + 1)/(-1 + x)^2/(-1 + x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 15 2014 *) PROG (MAGMA) [1/8*(2*n^3-2*n^2+5*n-(-1)^n*(n+1)+1): n in [1..50]]; // Vincenzo Librandi, Mar 15 2014 CROSSREFS Sequence in context: A184704 A295963 A221317 * A122751 A152944 A018437 Adjacent sequences:  A005995 A005996 A005997 * A005999 A006000 A006001 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Mar 15 2014 STATUS approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)