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a(n) = 30*n^2.
7

%I #28 Dec 02 2024 12:18:39

%S 0,30,120,270,480,750,1080,1470,1920,2430,3000,3630,4320,5070,5880,

%T 6750,7680,8670,9720,10830,12000,13230,14520,15870,17280,18750,20280,

%U 21870,23520,25230,27000,28830,30720,32670,34680,36750,38880,41070,43320,45630,48000,50430

%N a(n) = 30*n^2.

%C Sequence found by reading the line from 0, in the direction 0, 30, ..., in the square spiral whose vertices are the generalized 17-gonal numbers. - _Omar E. Pol_, Jul 03 2014

%H Vincenzo Librandi, <a href="/A244636/b244636.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.: 30*x*(1 + x)/(1 - x)^3. [corrected by _Bruno Berselli_, Jul 03 2014]

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

%F a(n) = 30*A000290(n) = 15*A001105(n) = 10*A033428(n) = 6*A033429(n) = 5*A033581(n) = 3*A033583(n) = 2*A064761(n). - _Omar E. Pol_, Jul 03 2014

%F From _Elmo R. Oliveira_, Dec 02 2024: (Start)

%F E.g.f.: 30*x*(1 + x)*exp(x).

%F a(n) = n*A249674(n) = A330451(3*n). (End)

%p A244636:=n->30*n^2: seq(A244636(n), n=0..50); # _Wesley Ivan Hurt_, Jul 04 2014

%t Table[30 n^2, {n, 0, 40}]

%t CoefficientList[Series[30x (1+x)/(1-x)^3,{x,0,50}],x] (* or *) LinearRecurrence[ {3,-3,1},{0,30,120},50] (* _Harvey P. Dale_, Dec 02 2021 *)

%o (Magma) [30*n^2: n in [0..40]];

%o (PARI) a(n)=30*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. similar sequences listed in A244630.

%Y Cf. A000290, A001105, A033428, A033429, A033581, A033583, A064761, A249674, A330451.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jul 03 2014