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%I #38 Dec 13 2022 02:08:14
%S 3,10,18,27,37,48,60,73,87,102,118,135,153,172,192,213,235,258,282,
%T 307,333,360,388,417,447,478,510,543,577,612,648,685,723,762,802,843,
%U 885,928,972,1017,1063,1110,1158,1207,1257,1308,1360,1413,1467,1522,1578
%N Truncated triangular numbers: a(n) = n*(n+1)/2 - 18.
%C If a 3-set Y and a 3-set Z, having one element in common, are subsets of an n-set X then a(n+2) is the number of 3-subsets of X intersecting both Y and Z. - _Milan Janjic_, Oct 03 2007
%H Colin Barker, <a href="/A051938/b051938.txt">Table of n, a(n) for n = 6..1000</a>
%H Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n + a(n-1) (with a(6)=3). - _Vincenzo Librandi_, Aug 06 2010
%F G.f.: x^6*(3*x^2-x-3) / (x-1)^3. - _Colin Barker_, Mar 18 2015
%F Sum_{n>=6} 1/a(n) = 4423/6120 + 2*Pi*tan(sqrt(145)*Pi/2)/sqrt(145). - _Amiram Eldar_, Dec 13 2022
%t Drop[Accumulate[Range[60]]-18,5] (* _Harvey P. Dale_, Dec 08 2017 *)
%o (PARI) Vec(x^6*(3*x^2-x-3)/(x-1)^3 + O(x^100)) \\ _Colin Barker_, Mar 18 2015
%Y a(n) = A000217(n) - 18 for n>5.
%Y Cf. A155212. - _Vincenzo Librandi_, Jan 22 2009
%K easy,nonn
%O 6,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
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