Voozh

A033429

a(n) = 5*n^2.

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

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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)

LINKS

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

Lancelot Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.

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)