OFFSET
0,2
COMMENTS
Also the number of 6-cycles in the (n+5)-triangular honeycomb acute knight graph. - Eric W. Weisstein, Jun 25 2017
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Graph Cycle.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = (15n^2 - 9n)/2 = A000566(n)*3.
a(n) = a(n-1)+15*n-12 with n>0, a(0)=0. - Vincenzo Librandi, Nov 26 2010
G.f.: 3*x*(1+4*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
a(0)=0, a(1)=3, a(2)=21, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, May 08 2012
a(n) = n + A226489(n). - Bruno Berselli, Jun 11 2013
Sum_{n>=1} 1/a(n) = tan(Pi/10)*Pi/9 - sqrt(5)*log(phi)/9 + 5*log(5)/18, where phi is the golden ratio (A001622). - Amiram Eldar, May 20 2023
MATHEMATICA
Table[3 n (5 n - 3)/2, {n, 0, 50}] (* Harvey P. Dale, May 08 2012 *)
LinearRecurrence[{3, -3, 1}, {0, 3, 21}, 50] (* Harvey P. Dale, May 08 2012 *)
CoefficientList[Series[-((3 x^5 (1 + 4 x))/(-1 + x)^3), {x, 0, 20}], x] (* Eric W. Weisstein, Jun 25 2017 *)
PROG
(PARI) a(n)=3*n*(5*n-3)/2 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152751, A152759, A152767, A153783, A153448, A153875.
Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=15: see Comments lines of A226492.
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Dec 13 2008
STATUS
approved