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A018214 Alkane (or paraffin) numbers l(13,n). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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: A061707 A253945 A056375 * 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

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.