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%I #8 Jul 01 2020 15:29:03
%S 3,11,19,27,35,43,54,65,81,97,113,129,148,167,186,210,234,258,285,312,
%T 339,366,398,430,465,500,535,570,605,645,688,731,774,817,860,903,954,
%U 1005,1056,1107,1158,1209,1263,1322,1381,1440,1499,1558,1620,1682,1749
%N Number of 6-element subsets of {1,2,3,...,n} for which the sum-set has 13 elements.
%H Colin Barker, <a href="/A112422/b112422.txt">Table of n, a(n) for n = 7..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,0,-1,0,0,0,0,-1,1).
%F G.f.: x^7*(3 +8*x +8*x^2 +8*x^3 +8*x^4 +8*x^5 +8*x^6) / ((1 -x)^3*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)). - Corrected by _Colin Barker_, Jan 10 2017
%t LinearRecurrence[{1,0,0,0,0,1,0,-1,0,0,0,0,-1,1},{3,11,19,27,35,43,54,65,81,97,113,129,148,167},60] (* _Harvey P. Dale_, Jul 01 2020 *)
%o (PARI) Vec(x^7*(3 +8*x +8*x^2 +8*x^3 +8*x^4 +8*x^5 +8*x^6) / ((1 -x)^3*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)) + O(x^60)) \\ _Colin Barker_, Jan 10 2017
%K nonn,easy
%O 7,1
%A _David S. Newman_, Dec 10 2005
%E Edited by _Colin Barker_, Jan 10 2017
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