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%I #10 Jan 11 2017 02:36:25
%S 6,24,42,60,78,96,114,138,162,198,234,270,306,342,384,426,468,522,576,
%T 630,684,744,804,864,924,996,1068,1140,1218,1296,1374,1452,1530,1620,
%U 1710,1806,1902,1998,2094,2190,2286,2394
%N Number of 6-element subsets of {1,2,3,...,n} which have a sum-set with 14 elements.
%H Colin Barker, <a href="/A112423/b112423.txt">Table of n, a(n) for n = 8..1000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,0,-1,0,0,0,0,0,-1,1).
%F G.f.: 6*x^8/((1-x)^2*(1-x^7))+12*x^9/((1-x)^2*(1-x^8)).
%t DeleteCases[#, 0] &@ CoefficientList[Series[6 x^8/((1 - x)^2 (1 - x^7)) + 12 x^9/((1 - x)^2 (1 - x^8)), {x, 0, 49}], x] (* _Michael De Vlieger_, Jan 10 2017 *)
%o (PARI) Vec(6*x^8*(1 +3*x +3*x^2 +3*x^3 +3*x^4 +3*x^5 +3*x^6 +3*x^7) / ((1 -x)^3*(1 +x)*(1 +x^2)*(1 +x^4)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)) + O(x^60)) \\ _Colin Barker_, Jan 10 2017
%K nonn,easy
%O 8,1
%A _David S. Newman_, Dec 10 2005
%E Edited by _Colin Barker_, Jan 10 2017
%E a(11) corrected by _Colin Barker_, Jan 10 2017
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