A033584 a(n) = 11*n^2.

0, 11, 44, 99, 176, 275, 396, 539, 704, 891, 1100, 1331, 1584, 1859, 2156, 2475, 2816, 3179, 3564, 3971, 4400, 4851, 5324, 5819, 6336, 6875, 7436, 8019, 8624, 9251, 9900, 10571, 11264, 11979, 12716

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

From Roberto E. Martinez II, Jan 07 2002: (Start)

Number of edges of the complete tripartite graph of order 7n, K_n,n,5n.

Number of edges of the complete tripartite graph of order 6n, K_n,2n,3n. (End)

11 times the squares. - Omar E. Pol, Dec 13 2008

Examples

			a(1)=22*1+0-11=11; a(2)=22*2+11-11=44; a(3)=22*3+44-11=99 - _Vincenzo Librandi_, Aug 05 2010
		

Links

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

Crossrefs

Cf. A000290, A008593, A195043.

Programs

Mathematica

Table[11*n^2, {n, 0, 35}] (* Amiram Eldar, Feb 03 2021 *)

PARI

a(n)=11*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 11*A000290(n). - Omar E. Pol, Dec 13 2008

a(n) = 22*n + a(n-1) - 11 (with a(0)=0). - Vincenzo Librandi, Aug 05 2010

From Amiram Eldar, Feb 03 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/66.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/132.

Product_{n>=1} (1 + 1/a(n)) = sqrt(11)*sinh(Pi/sqrt(11))/Pi.

Product_{n>=1} (1 - 1/a(n)) = sqrt(11)*sin(Pi/sqrt(11))/Pi. (End)

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

G.f.: 11*x*(1 + x)/(1-x)^3.

E.g.f.: 11*x*(1 + x)*exp(x).

a(n) = n*A008593(n) = A195043(2*n).

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