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A108928 a(n) = 8*n^2 - 3. 3

%I #26 Sep 08 2022 08:45:19

%S 5,29,69,125,197,285,389,509,645,797,965,1149,1349,1565,1797,2045,

%T 2309,2589,2885,3197,3525,3869,4229,4605,4997,5405,5829,6269,6725,

%U 7197,7685,8189,8709,9245,9797,10365,10949,11549,12165,12797,13445,14109,14789

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

%C Sequence found by reading the segment (5, 29) together with the line from 29, in the direction 29, 69,..., in the square spiral whose vertices are the triangular numbers A000217. - _Omar E. Pol_, Sep 04 2011

%H Vincenzo Librandi, <a href="/A108928/b108928.txt">Table of n, a(n) for n = 1..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) = 2*(2*n-1)*(2*n+1)-1.

%F a(1)=5, a(2)=29, a(3)=69, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Jul 21 2012

%F From _G. C. Greubel_, Jul 15 2017:(Start)

%F G.f.: x*(-5 - 14*x + 3*x^2)/(-1 + x)^3.

%F E.g.f.: (8*x^2 + 8*x - 3)*exp(x) + 3. (End)

%e (1*3 = 3)+2 = 5; (3*5 = 15)+14 = 29; (5*7 = 35)+34 = 69; (7*9 = 63)+62 = 125; ...

%p seq(8*n^2-3,n=1..50); # _Emeric Deutsch_, Aug 01 2005

%t 8*Range[50]^2-3 (* or *) LinearRecurrence[{3,-3,1},{5,29,69},50] (* _Harvey P. Dale_, Jul 21 2012 *)

%o (PARI) a(n)=8*n^2-3 \\ _Charles R Greathouse IV_, Sep 04 2011

%o (Magma) [8*n^2 - 3: n in [1..50]]; // _Vincenzo Librandi_, Sep 05 2011

%K easy,nonn

%O 1,1

%A Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jul 19 2005

%E More terms from _Emeric Deutsch_, Aug 01 2005

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)