OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).
FORMULA
a(n) = GCD of n-th and (n+1)st tetrahedral numbers (A000292). - Ross La Haye, Sep 13 2003
G.f.: (1 +2*x +10*x^2 +2*x^3 +x^4 -2*x^5 +x^8)/(1-x^3)^3.
a(n) = A234041(n+1) = A107711(n+4,3) = C(n+3,2)*gcd(n+4,3)/3 for n >= 0. See the o.g.f. of A234041. - Wolfdieter Lang, Feb 26 2014
a(n) = numerator of (n+2)*(n+3)/6. - Altug Alkan, Apr 18 2018
Sum_{n>=0} 1/a(n) = 5 - 4*Pi/(3*sqrt(3)). - Amiram Eldar, Aug 11 2022
a(n) = (n + 2)*(n + 3)*(5 - 2*A061347(n+1))/18. - Stefano Spezia, Oct 16 2023
MATHEMATICA
CoefficientList[Series[(1+2*x+10*x^2+2*x^3+x^4-2*x^5+x^8)/(1-x^3)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 04 2014 *)
PROG
(Magma) [Denominator(n*(n+5)/((n+2)*(n+3))): n in [0..60]]; // Vincenzo Librandi, Mar 04 2014
(PARI) a(n) = numerator((n+2)*(n+3)/6); \\ Altug Alkan, Apr 18 2018
(SageMath) [numerator(binomial(n+3, 2)/3) for n in (0..60)] # G. C. Greubel, Aug 04, 2022
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Mar 04 2014
STATUS
approved