%I #45 Jul 06 2021 07:40:09
%S 0,10,40,90,160,250,360,490,640,810,1000,1210,1440,1690,1960,2250,
%T 2560,2890,3240,3610,4000,4410,4840,5290,5760,6250,6760,7290,7840,
%U 8410,9000,9610,10240,10890,11560,12250,12960,13690,14440,15210,16000,16810
%N a(n) = 10*n^2.
%C 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
%C 10 times the squares. - _Omar E. Pol_, Dec 13 2008
%C 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
%H Nathaniel Johnston, <a href="/A033583/b033583.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 10*A000290(n) = 5*A001105(n) = 2*A033429(n). - _Omar E. Pol_, Dec 13 2008
%F a(n) = A158187(n) - 1. - _Reinhard Zumkeller_, Mar 13 2009
%F a(n) = 20*n + a(n-1) - 10 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 05 2010
%F 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
%F From _Amiram Eldar_, Feb 03 2021: (Start)
%F Sum_{n>=1} 1/a(n) = Pi^2/60.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/120.
%F Product_{n>=1} (1 + 1/a(n)) = sqrt(10)*sinh(Pi/sqrt(10))/Pi.
%F Product_{n>=1} (1 - 1/a(n)) = sqrt(10)*sin(Pi/sqrt(10))/Pi. (End)
%F From _Stefano Spezia_, Jul 06 2021: (Start)
%F O.g.f.: 10*x*(1 + x)/(1 - x)^3.
%F E.g.f.: 10*exp(x)*x*(1 + x). (End)
%p seq(10*n^2,n=0..41); # _Nathaniel Johnston_, Jun 26 2011
%t 10*Range[0,50]^2 (* _Harvey P. Dale_, Apr 20 2011 *)
%o (PARI) a(n)=10*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000217, A000290, A001105, A033428, A033429, A033581, A085787, A158187.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_