A033583 a(n) = 10*n^2.

0, 10, 40, 90, 160, 250, 360, 490, 640, 810, 1000, 1210, 1440, 1690, 1960, 2250, 2560, 2890, 3240, 3610, 4000, 4410, 4840, 5290, 5760, 6250, 6760, 7290, 7840, 8410, 9000, 9610, 10240, 10890, 11560, 12250, 12960, 13690, 14440, 15210, 16000, 16810

Offset

0,2

Comments

Number of edges of a complete 5-partite graph of order 5n, K_n,n,n,n,n. - Roberto E. Martinez II, Oct 18 2001

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

Sequence found by reading the line from 0, in the direction 0, 10, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = 10*A000290(n) = 5*A001105(n) = 2*A033429(n). - Omar E. Pol, Dec 13 2008

a(n) = A158187(n) - 1. - Reinhard Zumkeller, Mar 13 2009

a(n) = 20*n + a(n-1) - 10 for n>0, a(0)=0. - Vincenzo Librandi, Aug 05 2010

a(n) = t(5*n) - 5*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(5*n) - 5*A000217(n). - Bruno Berselli, Aug 31 2017

From Amiram Eldar, Feb 03 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/60.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/120.

Product_{n>=1} (1 + 1/a(n)) = sqrt(10)*sinh(Pi/sqrt(10))/Pi.

Product_{n>=1} (1 - 1/a(n)) = sqrt(10)*sin(Pi/sqrt(10))/Pi. (End)

From Stefano Spezia, Jul 06 2021: (Start)

O.g.f.: 10*x*(1 + x)/(1 - x)^3.

E.g.f.: 10*exp(x)*x*(1 + x). (End)

Maple

seq(10*n^2, n=0..41); # Nathaniel Johnston, Jun 26 2011

Mathematica

10*Range[0, 50]^2  (* Harvey P. Dale, Apr 20 2011 *)

Prog

(PARI) a(n)=10*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A000290, A001105, A033428, A033429, A033581, A085787, A158187.

Sequence in context: A210376 A359981 A060317 * A131037 A071233 A063490

Adjacent sequences: A033580 A033581 A033582 * A033584 A033585 A033586

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved