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A033429 a(n) = 5*n^2. 29
0, 5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 605, 720, 845, 980, 1125, 1280, 1445, 1620, 1805, 2000, 2205, 2420, 2645, 2880, 3125, 3380, 3645, 3920, 4205, 4500, 4805, 5120, 5445, 5780, 6125, 6480, 6845, 7220, 7605, 8000, 8405, 8820, 9245, 9680, 10125, 10580, 11045, 11520, 12005, 12500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of edges of the complete bipartite graph of order 6n, K_n,5n. - Roberto E. Martinez II, Jan 07 2002

Number of edges of the complete tripartite graph of order 4n, K_n,n,2n. - Roberto E. Martinez II, Jan 07 2002

a(n+1)-a(n) : 5, 15, 25, 35, 45, ... (see A017329). - Philippe Deléham, Dec 08 2011

From Larry J Zimmermann, Feb 21 2013: (Start)

The sum of the areas of 2 squares that equals the area of a rectangle with whole number sides using the formula x^2 + y^2 = (x+y+sqrt(2*x*y))(x+y-sqrt(2*x*y)), where the substitution y=2*x obtains the whole number sides of the rectangle. So x^2+(2*x)^2=5x(x).

  x     squares sum      rectangle (l,w)   area

  1     1,4     5                   5,1    5

  2     4,16    20                  10,2   20  (End)

REFERENCES

L. Hogben, Choice and Chance by Cardpack and Chessboard. Vol. 1, Chanticleer Press, NY, 1950, p. 36.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = 5*A000290(n). - Omar E. Pol, Dec 11 2008

From Bruno Berselli, Feb 11 2011: (Start)

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

a(n) = 4*A000217(n) + A000567(n). (End)

a(n) = a(n-1)+5*(2*n-1) (with a(0)=0). - Vincenzo Librandi, Nov 17 2010

a(n) = A131242(10*n+4). - Philippe Deléham, Mar 27 2013

a(n) = a(n-1) + 10*n - 5, with a(0)=0. - Jean-Bernard François, Oct 04 2013

a(n) = A001105(n) + A033428(n). - Altug Alkan, Sep 28 2015

E.g.f.: 5*x*(x+1)*exp(x). - G. C. Greubel, Jul 17 2017

MATHEMATICA

5*Range[50]^2 (* Alonso del Arte, May 23 2012 *)

PROG

(PARI) a(n)=5*n^2

CROSSREFS

Central column of A055096.

Cf. A000290.

Cf. numbers of the form  n*(d*n+10-d)/2:  A008587, A056000, A028347, A140090, A014106, A028895, A045944, A186029, A007742, A022267, A022268, A049452, A186030, A135703, A152734, A139273.

Cf. A185019.

Cf. A001105, A033428.

Sequence in context: A228168 A178977 A061188 * A168011 A160749 A147002

Adjacent sequences:  A033426 A033427 A033428 * A033430 A033431 A033432

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

EXTENSIONS

Better description from N. J. A. Sloane, May 15 1998

STATUS

approved

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Last modified November 20 04:05 EST 2017. Contains 294959 sequences.