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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 (list; graph; refs; listen; history; text; internal format)
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

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

FORMULA

2*(A005994(n)[ 1, 3, 9, 19, 38, 66, 110... ] + C(n, 4)[ 1, 5, 15, 35... ]).

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

4*A007009.

Cf. A005994, A005997.

Sequence in context: A174836 A244252 A050616 * A261977 A100625 A203248

Adjacent sequences:  A006006 A006007 A006008 * A006010 A006011 A006012

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 18 12:21 EST 2017. Contains 294891 sequences.