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A010002 a(0) = 1, a(n) = 9*n^2 + 2 for n>0. 2

%I

%S 1,11,38,83,146,227,326,443,578,731,902,1091,1298,1523,1766,2027,2306,

%T 2603,2918,3251,3602,3971,4358,4763,5186,5627,6086,6563,7058,7571,

%U 8102,8651,9218,9803,10406,11027,11666,12323,12998,13691,14402,15131,15878,16643

%N a(0) = 1, a(n) = 9*n^2 + 2 for n>0.

%C Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=1, s=2. After 1, all terms are in A000408. [_Bruno Berselli_, Feb 06 2012]

%C The identity (18*n^2+2)^2-(9*n^2+2)*(6*n)^2 = 4 can be written as A010008(n+1)^2-a(n+1)*A008588(n+1)^2 = 4. - _Vincenzo Librandi_, Feb 07 2012

%H Bruno Berselli, <a href="/A010002/b010002.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (1+x)*(1+7*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012

%F E.g.f.: (x*(x+1)*9+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012

%t Join[{1}, 9 Range[43]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)

%t Join[{1}, LinearRecurrence[{3, -3, 1}, {11, 38, 83}, 50]] (* _Vincenzo Librandi_, Aug 03 2015 *)

%o (PARI) A010002(n)=9*n^2+2-!n \\ _M. F. Hasler_, Feb 14 2012

%o (MAGMA) [1] cat [9*n^2+2: n in [1..50]]; // _Vincenzo Librandi_, Aug 03 2015

%Y Cf. A206399.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Bruno Berselli_, Feb 06 2012

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Last modified May 22 06:32 EDT 2019. Contains 323478 sequences. (Running on oeis4.)