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 numbersA085787.-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) =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
FromAmiram 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)
FromStefano 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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved