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%I #35 Sep 08 2022 08:45:42
%S 17,66,147,260,405,582,791,1032,1305,1610,1947,2316,2717,3150,3615,
%T 4112,4641,5202,5795,6420,7077,7766,8487,9240,10025,10842,11691,12572,
%U 13485,14430,15407,16416,17457,18530,19635,20772,21941,23142,24375,25640
%N a(n) = 16n^2 + n.
%C The identity (2048*n^2+128*n+1)^2 - (16*n^2+n)*(512*n+16)^2 = 1 can be written as A157476(n)^2 - a(n)*A157475(n)^2 = 1 (see also second comment in A157476).
%C Sequence found by reading the line from 17, in the direction 17, 66,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 02 2012
%H Vincenzo Librandi, <a href="/A157474/b157474.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A173511(2*n). - _Reinhard Zumkeller_, Feb 20 2010
%F a(1)=17, a(2)=66, a(3)=147, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Nov 08 2011
%F G.f.: x*(17 + 14*x + 3*x^2 - 3*x^3 + x^4)/(1-x)^3. - _Vincenzo Librandi_, Jan 01 2015
%t Table[16n^2+n,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{17,66,147},50] (* _Harvey P. Dale_, Nov 08 2011 *)
%t CoefficientList[Series[(17 + 14 x + 3 x^2 - 3 x^3 + x^4) / (1-x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jan 01 2015 *)
%o (PARI) a(n)=16*n^2+n \\ _Charles R Greathouse IV_, Feb 09 2012
%o (Magma) [16*n^2 + n: n in [1..40]]; // _Vincenzo Librandi_, Jan 01 2015
%Y Cf. A157475, A157476.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 01 2009
%E Comment rewritten by _Bruno Berselli_, Aug 22 2011
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