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A153037 a(n) = 2*n^2 + 16*n + 23.

%I A153037 #41 Feb 09 2025 00:23:20
%S A153037 23,41,63,89,119,153,191,233,279,329,383,441,503,569,639,713,791,873,
%T A153037 959,1049,1143,1241,1343,1449,1559,1673,1791,1913,2039,2169,2303,2441,
%U A153037 2583,2729,2879,3033,3191,3353,3519,3689,3863,4041,4223,4409,4599,4793,4991,5193
%N A153037 a(n) = 2*n^2 + 16*n + 23.
%C A153037 Sixth diagonal of triangle A154685.
%C A153037 Numbers of the form 2*k^2 - 9. - _Bruno Berselli_, Oct 30 2012
%H A153037 Vincenzo Librandi, <a href="/A153037/b153037.txt">Table of n, a(n) for n = 0..1000</a>
%H A153037 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153037 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 22 2012
%F A153037 G.f.: (23 - 28*x + 9*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jan 04 2013
%F A153037 From _Amiram Eldar_, Feb 25 2023: (Start)
%F A153037 Sum_{n>=0} 1/a(n) = 137/126 - cot(3*Pi/sqrt(2))*Pi/(6*sqrt(2)).
%F A153037 Sum_{n>=0} (-1)^n/a(n) = 43/42 - cosec(3*Pi/sqrt(2))*Pi/(6*sqrt(2)). (End)
%F A153037 E.g.f.: exp(x)*(23 + 18*x + 2*x^2). - _Elmo R. Oliveira_, Feb 08 2025
%t A153037 Table[2*n^2 + 16*n + 23, {n, 0, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 03 2012 *)
%t A153037 LinearRecurrence[{3, -3, 1}, {23, 41, 63}, 50] (* _Vincenzo Librandi_, Feb 22 2012 *)
%t A153037 CoefficientList[Series[(23 - 28*x  +9*x^2)/(1 -x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Jan 04 2013 *)
%o A153037 (PARI) a(n)=2*n^2+16*n+23 \\ _Charles R Greathouse IV_, Jan 11 2012
%o A153037 (Magma) I:=[23, 41, 63]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 22 2012
%Y A153037 Cf. A153039, A154685.
%K A153037 nonn,easy
%O A153037 0,1
%A A153037 _Vincenzo Librandi_, Jan 25 2009
%E A153037 Erroneously duplicated terms removed by _Vincenzo Librandi_, Feb 22 2012