A018214 Alkane (or paraffin) numbers l(13,n).

1, 6, 36, 146, 511, 1512, 4032, 9752, 21942, 46252, 92504, 176484, 323554, 572264, 981024, 1634776, 2656511, 4218786, 6562556, 10016006, 15024009, 22177584, 32258304, 46282704, 65567164, 91792792, 127097712, 174169352

Offset

0,2

References

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

Winston C. Yang (paper in preparation).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Classic Sequences

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)

Index entries for linear recurrences with constant coefficients, signature (6, -10, -10, 50, -34, -66, 110, 0, -110, 66, 34, -50, 10, 10, -6, 1).

Formula

l(c, r) = 1/2 C(c+r-3, r) + 1/2 d(c, r), where d(c, r) is C((c + r - 3)/2, r/2) if c is odd and r is even, 0 if c is even and r is odd, C((c + r - 4)/2, r/2) if c is even and r is even, C((c + r - 4)/2, (r - 1)/2) if c is odd and r is odd.

G.f.: -(5*x^4+10*x^2+1)/((x-1)^11*(x+1)^5). [Colin Barker, Aug 06 2012]

a(n) = (1/(2*10!))*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*((n+1)*(n+3)*(n+5)*(n+7)*(n+9) + 1*3*5*7*9)- (1/6)*(1/2^8)*(n^4+22*n^3+170*n^2+539*n+579)*(1/2)*(1-(-1)^n). [Yosu Yurramendi, Jun 23 2013]

Mathematica

CoefficientList[Series[-(5 x^4 + 10 x^2 + 1)/((x - 1)^11 (x + 1)^5), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 16 2013 *)
LinearRecurrence[{6, -10, -10, 50, -34, -66, 110, 0, -110, 66, 34, -50, 10, 10, -6, 1}, {1, 6, 36, 146, 511, 1512, 4032, 9752, 21942, 46252, 92504, 176484, 323554, 572264, 981024, 1634776}, 28] (* Ray Chandler, Sep 23 2015 *)

Prog

(Magma) [(1/(2*Factorial(10)))*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*((n+1)*(n+3)*(n+5)*(n+7)*(n+9)+1*3*5*7*9)-(1/6)*(1/2^8)*(n^4+22*n^3+170*n^2+539*n+579)*(1/2)*(1-(-1)^n): n in [0..40]]; // Vincenzo Librandi, Oct 16 2013

Crossrefs

Sequence in context: A360588 A321579 A364429 * A181478 A223841 A210322

Adjacent sequences: A018211 A018212 A018213 * A018215 A018216 A018217

Keyword

nonn,easy

Author

N. J. A. Sloane, Winston C. Yang (yang(AT)math.wisc.edu)

Status

approved