A089207 a(n) = 4*n^3 + 2*n^2.

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

Offset

1,1

Comments

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From R. J. Mathar, Apr 20 2009: (Start)

a(n) = 2*A099721(n).

a(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. (End)

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

E.g.f.: 2*x*(2*x + 1)*(x + 3)*exp(x). - Elmo R. Oliveira, May 27 2026

Mathematica

Table[4n^3+2n^2, {n, 40}] (* Harvey P. Dale, Jun 12 2020 *)

Crossrefs

Cf. A014105, A085409, A087887, A099721.

Sequence in context: A229638 A210291 A336317 * 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