A153796 6 times octagonal numbers: a(n) = 6*n*(3*n-2).

0, 6, 48, 126, 240, 390, 576, 798, 1056, 1350, 1680, 2046, 2448, 2886, 3360, 3870, 4416, 4998, 5616, 6270, 6960, 7686, 8448, 9246, 10080, 10950, 11856, 12798, 13776, 14790, 15840, 16926, 18048, 19206, 20400, 21630, 22896, 24198, 25536, 26910, 28320, 29766

Offset: 0

Author

Omar E. Pol, Jan 19 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000567, A139267, A152751.

Programs

Magma

[6*n*(3*n-2): n in [0..60]]; // Wesley Ivan Hurt, Aug 29 2016

Maple

A153796:=n->6*n*(3*n-2): seq(A153796(n), n=0..60); # Wesley Ivan Hurt, Aug 29 2016

Mathematica

s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,6,8!,36}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[6*n*(3*n-2), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,6,48}, 25] (* G. C. Greubel, Aug 29 2016 *)
6*PolygonalNumber[8,Range[0,50]] (* Harvey P. Dale, Dec 17 2023 *)

PARI

a(n)=6*n*(3*n-2) \\ Charles R Greathouse IV, Aug 29 2016

Formula

a(n) = 18*n^2 - 12*n = 6*A000567(n) = 3*A139267(n) = 2*A152751(n).

a(n) = a(n-1) + 36*n - 30 (with a(0)=0). - Vincenzo Librandi, Dec 15 2010

From G. C. Greubel, Aug 29 2016: (Start)

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

G.f.: 6*x*(1 + 5*x)/(1 - x)^3.

E.g.f.: 6*x*(1 + 3*x)*exp(x). (End)