A033582 a(n) = 7*n^2.

0, 7, 28, 63, 112, 175, 252, 343, 448, 567, 700, 847, 1008, 1183, 1372, 1575, 1792, 2023, 2268, 2527, 2800, 3087, 3388, 3703, 4032, 4375, 4732, 5103, 5488, 5887, 6300, 6727, 7168, 7623, 8092, 8575, 9072, 9583, 10108, 10647, 11200, 11767, 12348, 12943, 13552, 14175

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 bipartite graph of order 8n, K_n,7n.

Number of edges of the complete tripartite graph of order 5n, K_n,n,3n. (End)

Links

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

Crossrefs

Cf. A000290, A008589, A132111, A195041.

Programs

Mathematica

7Range[0, 49]^2 (* Alonso del Arte, Jun 30 2013 *)

PARI

a(n)=7*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

Central terms of the triangle in A132111: a(n) = A132111(2*n,n). - Reinhard Zumkeller, Aug 10 2007

a(n) = 7*A000290(n). - Omar E. Pol, Dec 11 2008

a(n) = 14*n + a(n-1) - 7 (with a(0) = 0). - Vincenzo Librandi, Aug 05 2010

G.f.: -7*x*(1+x)/(x-1)^3. - R. J. Mathar, Feb 06 2017

From Amiram Eldar, Feb 03 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/42.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/84.

Product_{n>=1} (1 + 1/a(n)) = sqrt(7)*sinh(Pi/sqrt(7))/Pi.

Product_{n>=1} (1 - 1/a(n)) = sqrt(7)*sin(Pi/sqrt(7))/Pi. (End)

From Elmo R. Oliveira, Dec 02 2024: (Start)

E.g.f.: 7*exp(x)*x*(1 + x).

a(n) = n*A008589(n) = A195041(2*n).

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