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%I #37 Dec 13 2022 02:18:41
%S 9,12,16,21,27,34,42,51,61,72,84,97,111,126,142,159,177,196,216,237,
%T 259,282,306,331,357,384,412,441,471,502,534,567,601,636,672,709,747,
%U 786,826,867,909,952,996,1041,1087,1134,1182,1231,1281,1332,1384,1437
%N a(n) = n*(n+3)/2 + 7.
%C Numbers m >= 9 such that 8*m - 47 is a square. - _Bruce J. Nicholson_, Jul 25 2017
%H Vincenzo Librandi, <a href="/A166136/b166136.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + n = 3*a(n-1) - 3*a(n-2) + a(n-3) = A145018(n+2) + 2.
%F G.f.: -x*(9 - 15*x + 7*x^2)/(x-1)^3.
%F E.g.f.: (1/2)*(14 + 4*x + x^2)*exp(x) - 7. - _G. C. Greubel_, Apr 26 2016
%F Sum_{n>=1} 1/a(n) = -13/42 + 2*Pi*tanh(sqrt(47)*Pi/2)/sqrt(47). - _Amiram Eldar_, Dec 13 2022
%t Table[n*(n+3)/2+7, {n, 1, 40}] (* or *) LinearRecurrence[{3,-3,1}, {9, 12, 16}, 40] (* _Vincenzo Librandi_, Mar 15 2012 *)
%o (Magma) I:=[9, 12, 16]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Mar 15 2012
%o (PARI) for(n=1, 40, print1(n*(n+3)/2+7, ", ")); \\ _Vincenzo Librandi_, Mar 15 2012
%Y Cf. A145018.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Oct 08 2009
%E Definition replaced by polynomial from _R. J. Mathar_, Oct 12 2009
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