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7 times octagonal numbers: a(n) = 7*n*(3*n-2).
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%I #18 Sep 08 2022 08:45:40

%S 0,7,56,147,280,455,672,931,1232,1575,1960,2387,2856,3367,3920,4515,

%T 5152,5831,6552,7315,8120,8967,9856,10787,11760,12775,13832,14931,

%U 16072,17255,18480,19747,21056,22407,23800,25235,26712,28231

%N 7 times octagonal numbers: a(n) = 7*n*(3*n-2).

%H G. C. Greubel, <a href="/A153797/b153797.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(n) = 21*n^2 - 14*n = 7*A000567(n).

%F a(n) = a(n-1) + 42*n - 35 (with a(0)=0). - _Vincenzo Librandi_, Nov 27 2010

%F From _G. C. Greubel_, Aug 29 2016: (Start)

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

%F G.f.: 7*x*(1 + 5*x)/(1 - x)^3.

%F E.g.f.: 7*x*(1 + 3*x)*exp(x). (End)

%t s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,7,8!,42}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2009 *)

%t Table[7*n*(3*n-2), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,7,56},25] (* _G. C. Greubel_, Aug 29 2016 *)

%o (Magma) [ 7*n*(3*n-2): n in [0..40] ];

%o (PARI) a(n)=7*n*(3*n-2) \\ _Charles R Greathouse IV_, Aug 29 2016

%Y Cf. A000567 (octagonal numbers), A153796, A153808.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Jan 20 2009