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a(n) = 17*n + 7.
2

%I #28 May 31 2024 05:47:23

%S 7,24,41,58,75,92,109,126,143,160,177,194,211,228,245,262,279,296,313,

%T 330,347,364,381,398,415,432,449,466,483,500,517,534,551,568,585,602,

%U 619,636,653,670,687,704,721,738,755,772,789,806,823,840,857,874,891

%N a(n) = 17*n + 7.

%C a(n)^4 = Sum_{j=0..(16*n*(17*n+14)+46)} (-1)^j*(119*n^2 + 98*n + 20 + j)^2. - _Bruno Berselli_, Apr 30 2010

%H Vincenzo Librandi, <a href="/A154612/b154612.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: (7+10*x)/(1-x)^2. - _Colin Barker_, Jan 09 2012

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 26 2012

%F E.g.f.: (7 + 17*x)*exp(x). - _G. C. Greubel_, May 31 2024

%e For n=5, a(5)^4 = 92^4 = 71639296 = 3485^2-3486^2+3487^2-..+11449^2-11450^2+11451^2. - _Bruno Berselli_, Apr 30 2010

%t Range[7, 1000, 17] (* _Vladimir Joseph Stephan Orlovsky_, Jun 01 2011 *)

%o (Magma) I:=[7, 24]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 21 2012

%o (PARI) for(n=0, 50, print1(17*n + 7", ")); \\ _Vincenzo Librandi_, Feb 26 2012

%o (SageMath) [17*n+7 for n in range(61)] # _G. C. Greubel_, May 31 2024

%Y Cf. A138629, A138630.

%Y Sequences of the form 17*n+q: A361692 (q=-1), A008599 (q=0), A215137 (q=1), this sequence (q=7).

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Jan 15 2009

%E Offset corrected by _Bruno Berselli_, Aug 16 2010