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 A018212 Alkane (or paraffin) numbers l(11,n). 2
 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 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 (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 Cf. A282011. 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 4 13:20 EST 2023. Contains 367562 sequences. (Running on oeis4.)