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A152746 Six times hexagonal numbers: 6*n*(2*n-1). 12
0, 6, 36, 90, 168, 270, 396, 546, 720, 918, 1140, 1386, 1656, 1950, 2268, 2610, 2976, 3366, 3780, 4218, 4680, 5166, 5676, 6210, 6768, 7350, 7956, 8586, 9240, 9918, 10620, 11346, 12096, 12870, 13668, 14490, 15336, 16206, 17100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 6, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Sep 18 2011

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 12*n^2 - 6*n = A000384(n)*6 = A002939(n)*3 = A094159(n)*2.

a(n) = a(n-1) + 24*n - 18 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010

From G. C. Greubel, Sep 01 2018: (Start)

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

E.g.f.: 6*x*(1+2*x)*exp(x). (End)

MATHEMATICA

6*PolygonalNumber[6, Range[0, 40]] (* The program uses the PolygonalNumber function from Mathematica version 10 *) (* Harvey P. Dale, Mar 04 2016 *)

LinearRecurrence[{3, -3, 1}, {0, 6, 36}, 50] (* or *) Table[6*n*(2*n-1), {n, 0, 50}] (* G. C. Greubel, Sep 01 2018 *)

PROG

(PARI) a(n)=6*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017

(MAGMA) [6*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Sep 01 2018

CROSSREFS

Cf. A000384, A002939, A094159, A085250, A152745.

Sequence in context: A207896 A207656 A207341 * A207363 A207600 A207026

Adjacent sequences:  A152743 A152744 A152745 * A152747 A152748 A152749

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Dec 12 2008

STATUS

approved

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Last modified November 21 08:42 EST 2018. Contains 317430 sequences. (Running on oeis4.)