A064761 a(n) = 15*n^2.

0, 15, 60, 135, 240, 375, 540, 735, 960, 1215, 1500, 1815, 2160, 2535, 2940, 3375, 3840, 4335, 4860, 5415, 6000, 6615, 7260, 7935, 8640, 9375, 10140, 10935, 11760, 12615, 13500, 14415, 15360, 16335, 17340, 18375, 19440, 20535, 21660, 22815

Offset: 0

Author

Roberto E. Martinez II, Oct 18 2001

Keywords

• nonn
• easy

Comments

Number of edges in a complete 6-partite graph of order 6n, K_n,n,n,n,n,n.

Links

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

Crossrefs

Cf. A000217, A000290, A008585, A008587, A022272, A033428, A033429, A033581, A033583.

Cf. A008597, A195046.

Programs

Mathematica

Table[15*n^2, {n, 0, 45}] (* Amiram Eldar, Feb 03 2021 *)

PARI

a(n)=15*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 15*A000290(n) = 5*A033428(n) = 3*A033429(n). - Omar E. Pol, Dec 13 2008

a(n) = A008587(n)*A008585(n). - Reinhard Zumkeller, Apr 12 2010

a(n) = a(n-1) + 30*n - 15 for n > 0, a(0)=0. - Vincenzo Librandi, Dec 15 2010

a(n) = A022272(n) + A022272(-n). - Bruno Berselli, Mar 31 2015

a(n) = t(6*n) - 6*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(6*n) - 6*A000217(n). - Bruno Berselli, Aug 31 2017

From Amiram Eldar, Feb 03 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/90.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/180.

Product_{n>=1} (1 + 1/a(n)) = sqrt(15)*sinh(Pi/sqrt(15))/Pi.

Product_{n>=1} (1 - 1/a(n)) = sqrt(15)*sin(Pi/sqrt(15))/Pi. (End)

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: 15*x*(1 + x)/(1 - x)^3.

E.g.f.: 15*x*(1 + x)*exp(x).

a(n) = n*A008597(n) = A195046(2*n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)