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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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 *)

PARI

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

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)