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a(n) = 29 + 73*n + 37*n^2.
2

%I #26 Sep 08 2022 08:45:38

%S 29,139,323,581,913,1319,1799,2353,2981,3683,4459,5309,6233,7231,8303,

%T 9449,10669,11963,13331,14773,16289,17879,19543,21281,23093,24979,

%U 26939,28973,31081,33263,35519,37849,40253,42731,45283,47909,50609,53383,56231,59153,62149,65219,68363

%N a(n) = 29 + 73*n + 37*n^2.

%H Vincenzo Librandi, <a href="/A145980/b145980.txt">Table of n, a(n) for n = 0..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) = A061037(4n+2)+A061037(4n+3)+A061037(4n+4)+A061037(4n+5).

%F From _R. J. Mathar_, Oct 31 2008 (Start)

%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).

%F G.f.: (29+52*x-7*x^2)/(1-x)^3. (End)

%F E.g.f.: (37*x^2 + 110*x + 29)*exp(x). - _G. C. Greubel_, Jan 29 2016

%t LinearRecurrence[{3, -3, 1}, {29, 139, 323}, 50] (* _G. C. Greubel_, Jan 29 2016 *)

%o (Magma) [29+73*n+37*n^2: n in [0..40]]; // _Vincenzo Librandi_, Aug 07 2011

%o (PARI) a(n)=29+73*n+37*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Oct 26 2008

%E Indices in definition edited, extended beyond a(13) by _R. J. Mathar_, Oct 31 2008