A153808 - OEIS

%I #18 Nov 22 2023 15:01:35

%S 0,8,64,168,320,520,768,1064,1408,1800,2240,2728,3264,3848,4480,5160,

%T 5888,6664,7488,8360,9280,10248,11264,12328,13440,14600,15808,17064,

%U 18368,19720,21120,22568,24064,25608,27200,28840,30528,32264

%N 8 times octagonal numbers: 8*n*(3*n-2).

%H G. C. Greubel, <a href="/A153808/b153808.txt">Table of n, a(n) for n = 0..999</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 24*n^2 - 16*n = 8*A000567(n) = 4*A139267(n) = 2*A153794(n).

%F a(n) = a(n-1) + 48*n - 40 (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.: 8*x*(1 + 5*x)/(1 - x)^3.

%F E.g.f.: 8*x*(1 + 3*x)*exp(x). (End)

%t Table[8*n*(3*n-2), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,8,64}, 25] (* _G. C. Greubel_, Aug 29 2016 *)

%t 8*PolygonalNumber[8,Range[0,40]] (* _Harvey P. Dale_, Nov 22 2023 *)

%o (Magma) [ 8*n*(3*n-2): n in [0..40] ];

%o (PARI) a(n)=24*n^2-16*n \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000567 (octagonal numbers), A064201 (9 times octagonal numbers), A139267 (twice octagonal numbers), A152751 (3 times octagonal numbers), A153794 (4 times octagonal numbers).

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Jan 19 2009