A202804 a(n) = n*(6*n+4).
0, 10, 32, 66, 112, 170, 240, 322, 416, 522, 640, 770, 912, 1066, 1232, 1410, 1600, 1802, 2016, 2242, 2480, 2730, 2992, 3266, 3552, 3850, 4160, 4482, 4816, 5162, 5520, 5890, 6272, 6666, 7072, 7490, 7920, 8362, 8816, 9282, 9760, 10250, 10752, 11266, 11792, 12330
Offset: 0
Links
- Jeremy Gardiner, Table of n, a(n) for n = 0..3000
- Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
- Leo Tavares, Illustration: Star Halves.
- Pavlos Vavolas, Cellular automaton model of cardiac arrhythmias, University of Sheffield Department of Computer Science (2005), (see page 43). [broken link, abstract]
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
-
Maple
A202804:=n->n*(6*n+4): seq(A202804(n), n=0..100); # Wesley Ivan Hurt, Apr 09 2017
-
Mathematica
Table[n(6n+4),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,10,32},50] (* Harvey P. Dale, Dec 28 2015 *) -
PARI
x='x + O('x^50); concat([0], Vec(-2*x*(5 + x)/(x - 1)^3)) \\ Indranil Ghosh, Apr 10 2017
Formula
a(n) = 2*n(3*n+2) = 6*n^2 + 4*n = 2*A045944(n).
a(n) = A080859(n) - 1. - Omar E. Pol, Jul 18 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 28 2015
G.f.: 2*x*(5 + x)/(1 - x)^3. - Indranil Ghosh, Apr 10 2017
From Amiram Eldar, Mar 01 2022: (Start)
Sum_{n>=1} 1/a(n) = (Pi/sqrt(3) - 3*log(3) + 3)/8.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(4*sqrt(3)) - 3/8. (End)
E.g.f.: 2*exp(x)*x*(5 + 3*x). - Elmo R. Oliveira, Dec 12 2024
Comments