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

0,2

Comments

Number of edges of the complete bipartite graph of order 8n, K_n,7n - Roberto E. Martinez II, Jan 07 2002

Number of edges of the complete tripartite graph of order 5n, K_n,n,3n - Roberto E. Martinez II, Jan 07 2002

Links

Table of n, a(n) for n=0..45.

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

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A000290, A132111.

Sequence in context: A045551 A024844 A230285 * A176362 A358999 A008457

Adjacent sequences: A033579 A033580 A033581 * A033583 A033584 A033585

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved