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A018212 Alkane (or paraffin) numbers l(11,n). 1
1, 5, 25, 85, 255, 651, 1519, 3235, 6470, 12190, 21942, 37854, 63090, 101850, 160050, 245322, 367983, 541035, 781495, 1110395, 1554553, 2146573, 2927145, 3945045, 5260060, 6942988, 9079292, 11769100, 15131700, 19305540 (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

Table of n, a(n) for n=0..29.

N. J. A. Sloane, Classic Sequences

Index entries for linear recurrences with constant coefficients, signature (5, -6, -10, 29, -9, -36, 36, 9, -29, 10, 6, -5, 1).

FORMULA

G.f.: (1+6*x^2+x^4)/((1-x)^5*(1-x^2)^4) [ N. J. A. Sloane ]

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

a(n) = (1/(2*8!))*(n+2)*(n+4)*(n+6)*(n+8)*((n+1)*(n+3)*(n+5)*(n+7) + 1*3*5*7) - (1/3)*(1/2^6)*(n^3+(27/2)*n^2+56*n+(279/4))*(1/2)*(1-(-1)^n) [Yosu Yurramendi Jun 23 2013]

MATHEMATICA

LinearRecurrence[{5, -6, -10, 29, -9, -36, 36, 9, -29, 10, 6, -5, 1}, {1, 5, 25, 85, 255, 651, 1519, 3235, 6470, 12190, 21942, 37854, 63090}, 30] (* Ray Chandler, Sep 23 2015 *)

CROSSREFS

Sequence in context: A147122 A051229 A058919 * A181477 A147274 A147034

Adjacent sequences:  A018209 A018210 A018211 * A018213 A018214 A018215

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified December 8 02:07 EST 2016. Contains 278902 sequences.