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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-Fran├žois 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

N. J. A. Sloane

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.)