OFFSET
0,2
COMMENTS
Number of edges of the complete tripartite graph of order 6n, K_n, n, 4n. - Roberto E. Martinez II, Jan 07 2002
Area of a square with side 3n. - Wesley Ivan Hurt, Sep 24 2014
Right-hand side of the binomial coefficient identity Sum_{k = 0..3*n} (-1)^(n+k+1)* binomial(3*n,k)*binomial(3*n + k,k)*(3*n - k) = a(n). - Peter Bala, Jan 12 2022
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..200
John Elias, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 9*n^2 = 9 * A000290(n). - Omar E. Pol, Dec 11 2008
a(n) = 3 * A033428(n). - Omar E. Pol, Dec 13 2008
a(n) = a(n-1) + 9*(2*n-1) for n>0, a(0)=0. - Vincenzo Librandi, Nov 19 2010
From Wesley Ivan Hurt, Sep 24 2014: (Start)
G.f.: 9*x*(1 + x)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n>3.
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/54.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/108.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/3)/(Pi/3).
Product_{n>=1} (1 - 1/a(n)) = sinh(Pi/2)/(Pi/2) = 3*sqrt(3)/(2*Pi) (A086089). (End)
a(n) = A051624(n) + 8*A000217(n). In general, if P(k,n) = the k-th n-gonal number, then (k*n)^2 = P(k^2 + 3,n) + (k^2 - 1)*A000217(n). - Charlie Marion, Mar 09 2022
MAPLE
MATHEMATICA
(3Range[0, 49])^2 (* Alonso del Arte, Sep 24 2014 *)
PROG
(Maxima) A016766(n):=(3*n)^2$
makelist(A016766(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(Magma) [(3*n)^2 : n in [0..50]]; // Wesley Ivan Hurt, Sep 24 2014
(PARI) a(n)=9*n^2 \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Zerinvary Lajos, May 30 2006
STATUS
approved