A106648 - OEIS

%I #16 Sep 08 2021 22:27:59

%S 8,17,32,53,80,113,152,197,248,305,368,437,512,593,680,773,872,977,

%T 1088,1205,1328,1457,1592,1733,1880,2033,2192,2357,2528,2705,2888,

%U 3077,3272,3473,3680,3893,4112,4337,4568,4805,5048,5297,5552,5813,6080,6353,6632

%N a(n) = 3*n^2 + 6*n + 8.

%H G. C. Greubel, <a href="/A106648/b106648.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 a(0)=8, a(1)=17, a(2)=32, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Sep 20 2012

%F G.f.: (8 -7*x +5*x^2)/(1-x)^3. - _R. J. Mathar_, Nov 07 2015

%F E.g.f.: (8 +9*x +3*x^2)*exp(x). - _G. C. Greubel_, Sep 08 2021

%t Table[3n^2+6n+8,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{8,17,32},50] (* _Harvey P. Dale_, Sep 20 2012 *)

%o (PARI) a(n)=3*n^2+6*n+8 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Sage) [3*(n+1)^2 + 5 for n in (0..50)] # _G. C. Greubel_, Sep 08 2021

%K nonn,easy

%O 0,1

%A MICK JOYCE (mjpj69(AT)msn.com), Jan 22 2006

%E Definition supplied by _Joshua Zucker_, Feb 01, 2006