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A006009
Number of paraffins.
(Formerly M3513)
3
4, 16, 48, 108, 216, 384, 640, 1000, 1500, 2160, 3024, 4116, 5488, 7168, 9216, 11664, 14580, 18000, 22000, 26620, 31944, 38016, 44928, 52728, 61516, 71344, 82320, 94500, 108000, 122880, 139264, 157216, 176868, 198288, 221616, 246924, 274360, 304000, 336000
OFFSET
1,1
REFERENCES
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
FORMULA
a(n) = 2*(A005994(n) + binomial(n, 4)).
G.f.: 4*x*(1-x^3) / ((1-x)^4*(1-x^2)^2). - Alois P. Heinz, Aug 13 2008
a(n) = Sum_{i=1..n} i*floor(i^2/2). - Enrique Pérez Herrero, Mar 10 2012
MAPLE
a:= n-> (Matrix([[0$4, 4, 16, 48, 108]]). Matrix(8, (i, j)-> if (i=j-1) then 1 elif j=1 then [4, -4, -4, 10, -4, -4, 4, -1][i] else 0 fi)^n)[1, 1]: seq(a(n), n=1..40); # Alois P. Heinz, Aug 13 2008
MATHEMATICA
a[n_] := 1/16*(2*n^4+12*n^3+24*n^2+2*(9-(-1)^n)*n-3*(-1)^n+3); Array[a, 40] (* Jean-François Alcover, Mar 17 2014 *)
CROSSREFS
Sequence in context: A308592 A050616 A297160 * A261977 A100625 A203248
KEYWORD
nonn,easy
STATUS
approved