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A089207 a(n) = 4n^3 + 2n^2. 0
6, 40, 126, 288, 550, 936, 1470, 2176, 3078, 4200, 5566, 7200, 9126, 11368, 13950, 16896, 20230, 23976, 28158, 32800, 37926, 43560, 49726, 56448, 63750, 71656, 80190, 89376, 99238, 109800, 121086, 133120, 145926, 159528, 173950, 189216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Yet another parametric representation of the solutions of the Diophantine equation x^2 - y^2 = z^3 is (3n^3, n^3, 2n^2). By taking the sum x+y+z we get a(n) = 4n^3 + 2n^2.

If Y is a 3-subset of an 2n-set X then, for n>=5, a(n-2) is the number of 5-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n)=2*A099721(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: 2*x*(3+8*x+x^2)/(x-1)^4. [R. J. Mathar, Apr 20 2009]

a(n) = 2 * n * A014105(n). - Richard R. Forberg, Jun 16 2013

CROSSREFS

Cf. A085409, A087887.

Sequence in context: A263956 A229638 A210291 * A318169 A027777 A227013

Adjacent sequences:  A089204 A089205 A089206 * A089208 A089209 A089210

KEYWORD

nonn,easy

AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 09 2003

EXTENSIONS

More terms from Ray Chandler, Feb 15 2004

STATUS

approved

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Last modified February 21 22:10 EST 2020. Contains 332113 sequences. (Running on oeis4.)