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A014642 Even octagonal numbers: 4*n*(3*n-1). 15
0, 8, 40, 96, 176, 280, 408, 560, 736, 936, 1160, 1408, 1680, 1976, 2296, 2640, 3008, 3400, 3816, 4256, 4720, 5208, 5720, 6256, 6816, 7400, 8008, 8640, 9296, 9976, 10680, 11408, 12160, 12936, 13736, 14560, 15408, 16280, 17176, 18096, 19040, 20008, 21000, 22016 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

8 times pentagonal numbers. - Omar E. Pol, Dec 11 2008

Sequence found by reading the line from 0, in the direction 0, 8, ..., in the square spiral whose vertices are the generalized octagonal A001082. - Omar E. Pol, Jul 18 2012

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).

FORMULA

a(n) = A000326(n)*8. - Omar E. Pol, Dec 11 2008

a(n) = A049450(n)*4 = A033579(n)*2. - Omar E. Pol, Dec 13 2008

a(n) = a(n-1) + 24*n - 16 (with a(0)=0). - Vincenzo Librandi, Nov 20 2010

G.f.: x*(8+16*x)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 06 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - G. C. Greubel, Jun 07 2017

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +8; AppendTo[lst, s], {n, 0, 8!, 24}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

LinearRecurrence[{3, -3, 1}, {0, 8, 40}, 50] (* G. C. Greubel, Jun 07 2017 *)

PROG

(PARI) for(n=0, 25, print1(4*n*(3*n-1), ", ")) \\ G. C. Greubel, Jun 07 2017

CROSSREFS

Cf. A000567, A014641, A014793, A014794, A033579, A000326, A049450.

Sequence in context: A207360 A226904 A069083 * A211631 A279273 A143943

Adjacent sequences:  A014639 A014640 A014641 * A014643 A014644 A014645

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from Patrick De Geest

STATUS

approved

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Last modified February 23 17:41 EST 2018. Contains 299584 sequences. (Running on oeis4.)