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%I #23 Jun 28 2023 21:56:09
%S 1,5,25,85,255,651,1519,3235,6470,12190,21942,37854,63090,101850,
%T 160050,245322,367983,541035,781495,1110395,1554553,2146573,2927145,
%U 3945045,5260060,6942988,9079292,11769100,15131700,19305540
%N Alkane (or paraffin) numbers l(11,n).
%D S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
%D Winston C. Yang (paper in preparation).
%H N. J. A. Sloane, <a href="/classic.html#LOSS">Classic Sequences</a>
%H S. M. Losanitsch, <a href="/A000602/a000602_1.pdf">Die Isomerie-Arten bei den Homologen der Paraffin-Reihe</a>, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (5, -6, -10, 29, -9, -36, 36, 9, -29, 10, 6, -5, 1).
%F G.f.: (1+6*x^2+x^4)/((1-x)^5*(1-x^2)^4). [ _N. J. A. Sloane_ ]
%F 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.
%F 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]
%t 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 *)
%Y Cf. A282011.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Winston C. Yang (yang(AT)math.wisc.edu)
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