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%I #48 Sep 08 2022 08:45:19
%S 5,13,23,35,49,65,83,103,125,149,175,203,233,265,299,335,373,413,455,
%T 499,545,593,643,695,749,805,863,923,985,1049,1115,1183,1253,1325,
%U 1399,1475,1553,1633,1715,1799,1885,1973,2063,2155,2249,2345,2443,2543,2645
%N a(n) = n^2 + 5*n - 1.
%C For n>1: a(n) = A176271(n+2,n-1). - _Reinhard Zumkeller_, Apr 13 2010
%C a(n-2) = n*(n + 1) - 7, n>=0, with a(-2) = -7, a(-1) = -5 and a(0) = -1, gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 29 for b = 2*n + 1. In general D = b^2 - 4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2. - _Wolfdieter Lang_, Aug 16 2013
%C Numbers m such that 4m+29 is an odd square, starting with 7^2 = A016754(3). - _Bruce J. Nicholson_, Jul 11 2017
%H Vincenzo Librandi, <a href="/A108195/b108195.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GreekCross.html">Greek Cross</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaullistCross.html">Gaullist Cross</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 2*n+a(n-1)+4, with n>1, a(1)=5. - _Vincenzo Librandi_, Nov 13 2010
%F G.f.: x*(5 + 3*x - x^2 - 5*x)/(1 - x)^3. - _Vincenzo Librandi_, Jun 11 2014
%e ....... +---+ ......... The Cross of Lorraine
%e ....... | + | ......... having n=2 crossbeams
%e ... +---+---+---+ ..... consists of a(2)=13 squares
%e ... | + | + | + |
%e ... +---+---+---+
%e ....... | + |
%e +---+---+---+---+---+
%e | + | + | + | + | + |
%e +---+---+---+---+---+
%e ....... | + |
%e ....... +---+
%e ....... | + |
%e ....... +---+
%e ....... | + |
%e ....... +---+
%p with (combinat):seq(fibonacci(3, n)+n-8, n=3..51); # _Zerinvary Lajos_, Jun 07 2008
%t CoefficientList[Series[(5 + 3 x - x^2 - 5 x)/(1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 11 2014 *)
%t Array[#^2 + 5 # - 1 &, 49] (* _Michael De Vlieger_, Jul 12 2017 *)
%o (Magma) [n^2+5*n-1: n in [1..40]]; // _Vincenzo Librandi_, Jun 11 2014
%o (PARI) a(n)=n^2+5*n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A002522.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, Jun 15 2005
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