OFFSET
0,2
COMMENTS
If Y is a 3-subset of an (2n+1)-set X then, for n>=4, a(n-1) is the number of 4-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007
Sequence found by reading the line (one of the diagonal axes) from 0, in the direction 0, 5,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
a(n) is the sum of 2*n consecutive integers starting from 2*n. - Bruno Berselli, Jan 16 2018
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n*(6*n-1).
G.f.: x*(5+7*x)/(1-x)^3.
a(n) = C(6*n,2)/3. - Zerinvary Lajos, Jan 02 2007
a(n) = A001105(n) + A033991(n) = A033428(n) + A049450(n) = A022266(n) + A000326(n). - Zerinvary Lajos, Jun 12 2007
a(n) = 12*n + a(n-1) - 7 for n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2, a(0)=0, a(1)=5, a(2)=22. - Harvey P. Dale, Mar 07 2012
E.g.f.: (6*x^2 + 5*x)*exp(x). - G. C. Greubel, Jul 17 2017
From Amiram Eldar, Jul 03 2020: (Start)
Sum_{n>=1} 1/a(n) = 2*log(2) + 3*log(3)/2 - sqrt(3)*Pi/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi - log(2) - 2*sqrt(3)*arccoth(sqrt(3)). (End)
MAPLE
seq(n*(6*n-1), n=0..42); # Zerinvary Lajos, Jun 12 2007
MATHEMATICA
Table[n(6n-1), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 5, 22}, 50] (* Harvey P. Dale, Mar 07 2012 *)
PROG
(PARI) a(n)=n*(6*n-1) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joe Keane (jgk(AT)jgk.org)
STATUS
approved